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Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

2020-02-19
Monairah Alansari , Rehan Ali , Mohammad Farid
Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a … Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.
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COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE

2016-01-01
Behzad Djafari-Rouhani , Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a … In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi-$$\phi $$-nonexpansive mapping in a Banach space

2021-05-10
Mohammad Farid , Watcharaporn Cholamjiak , Rehan Ali +1 more

An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

2021-11-29
Mohammad Farid , Rehan Ali , Watcharaporn Cholamjiak
In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem … In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.
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Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

2017-11-28
Mohammad Farid , Syed Shakaib Irfan , M. Firdosh Khan +1 more
In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions … In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.
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An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

2020-09-10
Monairah Alansari , Mohammad Farid , Rehan Ali
Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family … Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.
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A new mapping for finding a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem

2019-06-30
Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a … In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

The subgradient extragradient method for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

2019-01-01
Mohammad Farid
In this paper, we introduce an iterative method based on hybrid methods and hybrid extragradient methods for finding a common solution of mixed equilibrium problems and fixed point problems of … In this paper, we introduce an iterative method based on hybrid methods and hybrid extragradient methods for finding a common solution of mixed equilibrium problems and fixed point problems of nonexpansive mappings in a real Hilbert space.We define the notion of generalized skew-symmetric bifunctions which is a natural extension of a skew-symmetric bifunctions.Further, we prove that the sequences generated by the proposed iterative scheme converge strongly to a common solution of these systems.The results presented in this paper are the supplements, extensions and generalizations of the previously known results in this area.
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Some iterative schemes for generalized vector equilibrium problems and relatively nonexpansive mappings in Banach spaces

2013-01-01
K.R. Kazmi , Mohammad Farid

Two algorithms for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

2021-10-26
Mohammad Farid

Inertial iterative method for a generalized mixed equilibrium, variational inequality and a fixed point problems for a family of quasi-ϕ-nonexpansive mappings

2023-01-01
Mohammad Farid , Rehan Ali , K.R. Kazmi
We introduce an inertial type gradient projection hybrid iterative method for finding a common solution of generalized mixed equilibrium, variational inequality and fixed point problems in a twouniformly convex and … We introduce an inertial type gradient projection hybrid iterative method for finding a common solution of generalized mixed equilibrium, variational inequality and fixed point problems in a twouniformly convex and uniformly smooth Banach space. Next, we analyze the strong convergence for a common solution of problem. Furthermore, we carry out some consequences and present a numerical example to show and tell the applicability of main theorem. Our result improves, unifies, generalizes and extends ones from several earlier works.
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Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

2020-02-13
Iqbal Ahmad , Syed Shakaib Irfan , Mohammad Farid +1 more
Abstract In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has … Abstract In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has been recommended and solved by employing an iterative algorithm. We establish the equivalence between nonlinear fuzzy ordered variational inclusion problem and nonlinear fuzzy ordered resolvent equation problem. The existence and convergence analysis of the solution of nonlinear fuzzy ordered variational inclusion problem involving XOR operation has been substantiated by applying a new resolvent operator method with XOR operation technique. The iterative algorithm and results demonstrated in this article have witnessed a significant improvement in many previously known results of this domain.
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Extragradient method with inertial iterative technique for pseudomonotone split equilibrium and fixed point problems of new mappings

2023-12-26
Mohammad Farid , Pronpat Peeyada , Rehan Ali +1 more

A Study of Szász–Durremeyer-Type Operators Involving Adjoint Bernoulli Polynomials

2024-11-21
Nadeem Rao , Mohammad Farid , Rehan Ali
This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators … This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetre’s K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results.

Symmetric Properties of λ-Szász Operators Coupled with Generalized Beta Functions and Approximation Theory

2024-12-22
Nadeem Rao , Mohammad Farid , Mohd Raiz
This research work focuses on λ-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in λ-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of … This research work focuses on λ-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in λ-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approximation and convergence properties. The convergence properties, such as uniform convergence and pointwise convergence, are studied in view of the Korovkin theorem, the modulus of continuity, and Peetre’s K-functional of these sequences of positive linear operators in depth. Further, we extend our research work for the bivariate case of these sequences of operators. Their uniform rate of approximation and order of approximation are investigated in Lebesgue measurable spaces of function. The graphical representation and numerical error analysis in terms of the convergence behavior of these operators are studied.

Common solutions to some systems of vector equilibrium problems and common xed point problems in Banach space

2016-12-26
Mohammad Farid , K.R. Kazmi
In this paper, we study some properties of set of solutions of a new gen-eralized mixed vector equilibrium problem in Banach space. Further, we introduce aniterative method based on hybrid … In this paper, we study some properties of set of solutions of a new gen-eralized mixed vector equilibrium problem in Banach space. Further, we introduce aniterative method based on hybrid method and convex approximation method for nd-ing a common element to the set of solutions of a system of unrelated generalized mixedvector equilibrium problems and the set of solutions of common xed point problemsfor the two families of generalized asymptotically quasi -nonexpansive mappings inBanach space. Furthermore, we obtain a strong convergence theorem for the sequencesgenerated by the proposed iterative scheme. Finally, we derive some consequences fromour main result. The results presented in this paper extended and unify many of thepreviously known results in this area.

An inertial iterative algorithm for generalized equilibrium problems and Bregman relatively nonexpansive mappings in Banach spaces

2022-01-06
Monairah Alansari , Mohammad Farid , Rehan Ali
Abstract The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We … Abstract The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result.
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Iterative Algorithm of Split Monotone Variational Inclusion Problem for New Mappings

2024-01-01
Mohammad Farid , Syed Shakaib Irfan , Iqbal Ahmad
In this paper, we developed a new type iterative scheme to approximate a common solution of split monotone variational inclusion, variational inequality and fixed point problems for an infinite family … In this paper, we developed a new type iterative scheme to approximate a common solution of split monotone variational inclusion, variational inequality and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we proved that the sequence generated by the proposed iterative method converges strongly to a common solution of split monotone variational inclusion, variational inequality and fixed point problems. Furthermore, we give some consequences of the main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm. The result presented in this paper unifies and extends some known results in this area.
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Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued mappings in Banach space

2024-07-03
Saud Fahad Aldosary , Mohammad Farid
Abstract We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive … Abstract We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive multivalued mappings, and a variational inequality problem. Our discussion encompasses the strong convergence of the proposed algorithm and highlights specific outcomes derived from our theorem. Additionally, we provide a computational analysis to underscore the significance of our findings and draw comparisons. The results presented in this paper serve to extend and unify numerous previously established outcomes in this particular research domain.
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Existence and Iterative approximation of common solution of generalized equilibrium problems,generalized variational inequality problems and fixed point problems

2014-01-01
Mohammad Farid

Correction to: An iterative scheme for split monotone variational inclusion, variational inequality, and fixed point problems

2023-01-13
Monairah Alansari , Mohammad Farid , Rehan Ali
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Solving System of Mixed Ordered Variational Inequalities Involving XOR and XNOR Operations in Ordered Product Banach Space

2023-12-29
Iqbal Ahmad , Mohammad Farid , Syed Shakaib Irfan
In this article, we study a generalized system of mixed ordered variational inequalities problems with various operations in a real ordered product Banach space and discuss the existence of the … In this article, we study a generalized system of mixed ordered variational inequalities problems with various operations in a real ordered product Banach space and discuss the existence of the solution of our considered problem. Further, we discuss the convergence analysis of the proposed iterative algorithm using XNOR and XOR operations techniques. Most of the variational inequalities solved by the projection operator technique but we solved our considered problem without the projection technique. The results of this paper are more general and new than others in this direction. Finally, we give a numerical example to illustrate and show the convergence of the proposed algorithm in support of our main result has been formulated by using MATLAB programming. 2010 AMS Subject Classification: 47H09; 49J40.
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Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials

2025-03-27
Nadeem Rao , Mohammad Farid , Mohd Raiz
This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and … This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical Korovkin theorem and the modulus of continuity for Lebesgue measurable and continuous functions. A Voronovskaja-type theorem is also established to approximate functions with first- and second-order continuous derivatives. Numerical and graphical analyses are presented to support these findings. Furthermore, a bivariate sequence of these operators is introduced to approximate a bivariate class of Lebesgue measurable and continuous functions in two variables. Finally, numerical and graphical representations of the error are provided to check the rapidity of convergence.

A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions

2025-01-01
Saud Fahad Aldosary , Mohammad Farid

On the Approximations and Symmetric Properties of Frobenius–Euler–Şimşek Polynomials Connecting Szász Operators

2025-04-25
Nadeem Rao , Mohammad Farid , Mohd Raiz
This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. … This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. Next, we investigate approximation order uniform convergence via Korovkin result and the modulus of smoothness for functions in continuous functional spaces. A Voronovskaja theorem is also explored approximating functions which belongs to the class of function having first and second order continuous derivative. Further, we discuss numerical error and graphical analysis. In the last, two dimensional operators are constructed to discuss approximation for the class of two variable continuous functions.

Szász–Beta Operators Linking Frobenius–Euler–Simsek-Type Polynomials

2025-05-29
Nadeem Rao , Mohammad Farid , Shivani Bansal
This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for … This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for the Lebesgue integrable functions, i.e., Lp[0,∞), 1≤p<∞. Furthermore, estimates in view of test functions and central moments are studied. Next, rate of convergence is discussed with the aid of the Korovkin theorem and the Voronovskaja type theorem. Moreover, direct approximation results in terms of modulus of continuity of first- and second-order, Peetre’s K-functional, Lipschitz type space, and the rth-order Lipschitz type maximal functions are investigated. In the subsequent section, we present weighted approximation results, and statistical approximation theorems are discussed. To demonstrate the effectiveness and applicability of the proposed operators, we present several illustrative examples and visualize the results graphically.

On the Strong Convergence of Combined Generalized Equilibrium and Fixed Point Problems in a Banach Space

2025-05-30
Ghada AlNemer , Rehan Ali , Mohammad Farid
This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges … This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges strongly to a shared solution within a two-uniformly convex and uniformly smooth real Banach space. We also highlight some immediate consequences of the main result. To confirm the algorithm’s efficiency, a numerical example is provided. Furthermore, the practical utility of the proposed algorithm is illustrated using comprehensive tables and figures.

On the Strong Convergence of Combined Generalized Equilibrium and Fixed Point Problems in a Banach Space

2025-05-30
Ghada AlNemer , Rehan Ali , Mohammad Farid
This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges … This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges strongly to a shared solution within a two-uniformly convex and uniformly smooth real Banach space. We also highlight some immediate consequences of the main result. To confirm the algorithm’s efficiency, a numerical example is provided. Furthermore, the practical utility of the proposed algorithm is illustrated using comprehensive tables and figures.

Szász–Beta Operators Linking Frobenius–Euler–Simsek-Type Polynomials

2025-05-29
Nadeem Rao , Mohammad Farid , Shivani Bansal
This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for … This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for the Lebesgue integrable functions, i.e., Lp[0,∞), 1≤p<∞. Furthermore, estimates in view of test functions and central moments are studied. Next, rate of convergence is discussed with the aid of the Korovkin theorem and the Voronovskaja type theorem. Moreover, direct approximation results in terms of modulus of continuity of first- and second-order, Peetre’s K-functional, Lipschitz type space, and the rth-order Lipschitz type maximal functions are investigated. In the subsequent section, we present weighted approximation results, and statistical approximation theorems are discussed. To demonstrate the effectiveness and applicability of the proposed operators, we present several illustrative examples and visualize the results graphically.

On the Approximations and Symmetric Properties of Frobenius–Euler–Şimşek Polynomials Connecting Szász Operators

2025-04-25
Nadeem Rao , Mohammad Farid , Mohd Raiz
This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. … This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. Next, we investigate approximation order uniform convergence via Korovkin result and the modulus of smoothness for functions in continuous functional spaces. A Voronovskaja theorem is also explored approximating functions which belongs to the class of function having first and second order continuous derivative. Further, we discuss numerical error and graphical analysis. In the last, two dimensional operators are constructed to discuss approximation for the class of two variable continuous functions.

Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials

2025-03-27
Nadeem Rao , Mohammad Farid , Mohd Raiz
This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and … This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical Korovkin theorem and the modulus of continuity for Lebesgue measurable and continuous functions. A Voronovskaja-type theorem is also established to approximate functions with first- and second-order continuous derivatives. Numerical and graphical analyses are presented to support these findings. Furthermore, a bivariate sequence of these operators is introduced to approximate a bivariate class of Lebesgue measurable and continuous functions in two variables. Finally, numerical and graphical representations of the error are provided to check the rapidity of convergence.

A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions

2025-01-01
Saud Fahad Aldosary , Mohammad Farid

Symmetric Properties of λ-Szász Operators Coupled with Generalized Beta Functions and Approximation Theory

2024-12-22
Nadeem Rao , Mohammad Farid , Mohd Raiz
This research work focuses on λ-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in λ-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of … This research work focuses on λ-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in λ-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approximation and convergence properties. The convergence properties, such as uniform convergence and pointwise convergence, are studied in view of the Korovkin theorem, the modulus of continuity, and Peetre’s K-functional of these sequences of positive linear operators in depth. Further, we extend our research work for the bivariate case of these sequences of operators. Their uniform rate of approximation and order of approximation are investigated in Lebesgue measurable spaces of function. The graphical representation and numerical error analysis in terms of the convergence behavior of these operators are studied.

A Study of Szász–Durremeyer-Type Operators Involving Adjoint Bernoulli Polynomials

2024-11-21
Nadeem Rao , Mohammad Farid , Rehan Ali
This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators … This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetre’s K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results.

Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued mappings in Banach space

2024-07-03
Saud Fahad Aldosary , Mohammad Farid
Abstract We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive … Abstract We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive multivalued mappings, and a variational inequality problem. Our discussion encompasses the strong convergence of the proposed algorithm and highlights specific outcomes derived from our theorem. Additionally, we provide a computational analysis to underscore the significance of our findings and draw comparisons. The results presented in this paper serve to extend and unify numerous previously established outcomes in this particular research domain.
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Iterative Algorithm of Split Monotone Variational Inclusion Problem for New Mappings

2024-01-01
Mohammad Farid , Syed Shakaib Irfan , Iqbal Ahmad
In this paper, we developed a new type iterative scheme to approximate a common solution of split monotone variational inclusion, variational inequality and fixed point problems for an infinite family … In this paper, we developed a new type iterative scheme to approximate a common solution of split monotone variational inclusion, variational inequality and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we proved that the sequence generated by the proposed iterative method converges strongly to a common solution of split monotone variational inclusion, variational inequality and fixed point problems. Furthermore, we give some consequences of the main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm. The result presented in this paper unifies and extends some known results in this area.
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Solving System of Mixed Ordered Variational Inequalities Involving XOR and XNOR Operations in Ordered Product Banach Space

2023-12-29
Iqbal Ahmad , Mohammad Farid , Syed Shakaib Irfan
In this article, we study a generalized system of mixed ordered variational inequalities problems with various operations in a real ordered product Banach space and discuss the existence of the … In this article, we study a generalized system of mixed ordered variational inequalities problems with various operations in a real ordered product Banach space and discuss the existence of the solution of our considered problem. Further, we discuss the convergence analysis of the proposed iterative algorithm using XNOR and XOR operations techniques. Most of the variational inequalities solved by the projection operator technique but we solved our considered problem without the projection technique. The results of this paper are more general and new than others in this direction. Finally, we give a numerical example to illustrate and show the convergence of the proposed algorithm in support of our main result has been formulated by using MATLAB programming. 2010 AMS Subject Classification: 47H09; 49J40.
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Extragradient method with inertial iterative technique for pseudomonotone split equilibrium and fixed point problems of new mappings

2023-12-26
Mohammad Farid , Pronpat Peeyada , Rehan Ali +1 more

Correction to: An iterative scheme for split monotone variational inclusion, variational inequality, and fixed point problems

2023-01-13
Monairah Alansari , Mohammad Farid , Rehan Ali
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Inertial iterative method for a generalized mixed equilibrium, variational inequality and a fixed point problems for a family of quasi-ϕ-nonexpansive mappings

2023-01-01
Mohammad Farid , Rehan Ali , K.R. Kazmi
We introduce an inertial type gradient projection hybrid iterative method for finding a common solution of generalized mixed equilibrium, variational inequality and fixed point problems in a twouniformly convex and … We introduce an inertial type gradient projection hybrid iterative method for finding a common solution of generalized mixed equilibrium, variational inequality and fixed point problems in a twouniformly convex and uniformly smooth Banach space. Next, we analyze the strong convergence for a common solution of problem. Furthermore, we carry out some consequences and present a numerical example to show and tell the applicability of main theorem. Our result improves, unifies, generalizes and extends ones from several earlier works.
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An inertial iterative algorithm for generalized equilibrium problems and Bregman relatively nonexpansive mappings in Banach spaces

2022-01-06
Monairah Alansari , Mohammad Farid , Rehan Ali
Abstract The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We … Abstract The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result.
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An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

2021-11-29
Mohammad Farid , Rehan Ali , Watcharaporn Cholamjiak
In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem … In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.
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Two algorithms for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

2021-10-26
Mohammad Farid

A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi-$$\phi $$-nonexpansive mapping in a Banach space

2021-05-10
Mohammad Farid , Watcharaporn Cholamjiak , Rehan Ali +1 more

An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

2020-09-10
Monairah Alansari , Mohammad Farid , Rehan Ali
Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family … Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.
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Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

2020-02-19
Monairah Alansari , Rehan Ali , Mohammad Farid
Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a … Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.
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Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

2020-02-13
Iqbal Ahmad , Syed Shakaib Irfan , Mohammad Farid +1 more
Abstract In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has … Abstract In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has been recommended and solved by employing an iterative algorithm. We establish the equivalence between nonlinear fuzzy ordered variational inclusion problem and nonlinear fuzzy ordered resolvent equation problem. The existence and convergence analysis of the solution of nonlinear fuzzy ordered variational inclusion problem involving XOR operation has been substantiated by applying a new resolvent operator method with XOR operation technique. The iterative algorithm and results demonstrated in this article have witnessed a significant improvement in many previously known results of this domain.
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A new mapping for finding a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem

2019-06-30
Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a … In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

The subgradient extragradient method for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

2019-01-01
Mohammad Farid
In this paper, we introduce an iterative method based on hybrid methods and hybrid extragradient methods for finding a common solution of mixed equilibrium problems and fixed point problems of … In this paper, we introduce an iterative method based on hybrid methods and hybrid extragradient methods for finding a common solution of mixed equilibrium problems and fixed point problems of nonexpansive mappings in a real Hilbert space.We define the notion of generalized skew-symmetric bifunctions which is a natural extension of a skew-symmetric bifunctions.Further, we prove that the sequences generated by the proposed iterative scheme converge strongly to a common solution of these systems.The results presented in this paper are the supplements, extensions and generalizations of the previously known results in this area.
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Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

2017-11-28
Mohammad Farid , Syed Shakaib Irfan , M. Firdosh Khan +1 more
In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions … In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.
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Common solutions to some systems of vector equilibrium problems and common xed point problems in Banach space

2016-12-26
Mohammad Farid , K.R. Kazmi
In this paper, we study some properties of set of solutions of a new gen-eralized mixed vector equilibrium problem in Banach space. Further, we introduce aniterative method based on hybrid … In this paper, we study some properties of set of solutions of a new gen-eralized mixed vector equilibrium problem in Banach space. Further, we introduce aniterative method based on hybrid method and convex approximation method for nd-ing a common element to the set of solutions of a system of unrelated generalized mixedvector equilibrium problems and the set of solutions of common xed point problemsfor the two families of generalized asymptotically quasi -nonexpansive mappings inBanach space. Furthermore, we obtain a strong convergence theorem for the sequencesgenerated by the proposed iterative scheme. Finally, we derive some consequences fromour main result. The results presented in this paper extended and unify many of thepreviously known results in this area.

COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE

2016-01-01
Behzad Djafari-Rouhani , Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a … In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

Existence and Iterative approximation of common solution of generalized equilibrium problems,generalized variational inequality problems and fixed point problems

2014-01-01
Mohammad Farid

Some iterative schemes for generalized vector equilibrium problems and relatively nonexpansive mappings in Banach spaces

2013-01-01
K.R. Kazmi , Mohammad Farid
Coauthor Papers Together
Rehan Ali 10
K.R. Kazmi 6
Nadeem Rao 5
Monairah Alansari 4
Syed Shakaib Irfan 4
Mohd Raiz 3
Watcharaporn Cholamjiak 3
Iqbal Ahmad 2
Saud Fahad Aldosary 2
Preeti Shukla 1
Shivani Bansal 1
Iqbal Ahmad 1
Suhel Ahmad Khan 1
Pronpat Peeyada 1
M. Firdosh Khan 1
Behzad Djafari-Rouhani 1
Ghada AlNemer 1

On some non-linear elliptic differential-functional equations

1966-01-01
Philip Hartman , Guido Stampacchia
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Inequalities in Banach spaces with applications

1991-01-01
Hong–Kun Xu

Convergence theorems for inertial KM-type algorithms

2007-07-26
Paul-Émile Maingé

Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings

2016-12-20
Qiao‐Li Dong , Hongtai Yuan , Y. J. Cho +1 more

Strong Convergence of a Proximal-Type Algorithm in a Banach Space

2002-01-01
Shoji Kamimura , Wataru Takahashi
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistoryPublished online: 28 July 2006Keywordsproximal point algorithm, maximal monotone operator, Banach space, strong convergenceAMS … Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistoryPublished online: 28 July 2006Keywordsproximal point algorithm, maximal monotone operator, Banach space, strong convergenceAMS Subject Headings47H05, 47J25Publication DataISSN (print): 1052-6234ISSN (online): 1095-7189Publisher: Society for Industrial and Applied MathematicsCODEN: sjope8

Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

2009-06-17
Lu-Chuan Ceng , Nicolas Hadjisavvas , Ngai‐Ching Wong
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Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces

2007-12-05
Wataru Takahashi , Kei Zembayashi

Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems

2019-04-25
Qiao‐Li Dong , K.R. Kazmi , Rehan Ali +1 more

Weak convergence of the sequence of successive approximations for nonexpansive mappings

1967-01-01
Z. Opial
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A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi-$$\phi $$-nonexpansive mapping in a Banach space

2021-05-10
Mohammad Farid , Watcharaporn Cholamjiak , Rehan Ali +1 more

Strong Convergence Theorem by a Hybrid Method for Nonexpansive Mappings and Lipschitz-Continuous Monotone Mappings

2006-01-01
Natalia Nadezhkina , Wataru Takahashi
In this paper we introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the … In this paper we introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on two well-known methods: hybrid and extragradient. We obtain a strong convergence theorem for three sequences generated by this process. Based on this result, we also construct an iterative process for finding a common fixed point of two mappings, such that one of these mappings is nonexpansive and the other is taken from the more general class of Lipschitz pseudocontractive mappings.

Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces

2015-09-28
Kazuhide Nakajo

Second-order differential proximal methods for equilibrium problems

2003-01-28
Abdellatif Moudafi
An approximate procedure for solving equilibrium problems is proposed and its convergence is established under natural conditions. The result obtained in this paper includes, as a special case, some known … An approximate procedure for solving equilibrium problems is proposed and its convergence is established under natural conditions. The result obtained in this paper includes, as a special case, some known results in convex minimization and monotone inclusion fields.
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A new mapping for finding a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem

2019-06-30
Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a … In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces

2004-03-03
Shin-ya Matsushita , Wataru Takahashi
We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of … We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.
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Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces

2006-09-27
Satoru Takahashi , Wataru Takahashi

Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings

2006-01-01
Natalia Nadezhkina , Wataru Takahashi

Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

2020-02-19
Monairah Alansari , Rehan Ali , Mohammad Farid
Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a … Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.
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Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

2017-11-28
Mohammad Farid , Syed Shakaib Irfan , M. Firdosh Khan +1 more
In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions … In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.
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Common solution to an equilibrium problem and a fixed point problem for an asymptotically quasi- $$\phi $$ ϕ -nonexpansive mapping in intermediate sense

2016-09-01
K.R. Kazmi , Rehan Ali

A general iterative method for nonexpansive mappings in Hilbert spaces

2005-06-10
Giuseppe Marino , Hong–Kun Xu

Iterative Algorithms for Nonlinear Operators

2002-08-01
Hong‐Kun Xu
Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result of Lions. A modification of … Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result of Lions. A modification of Rockafellar's proximal point algorithm is obtained and proved to be always strongly convergent. The ideas of these algorithms are applied to solve a quadratic minimization problem.

A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

2007-03-02
Lu-Chuan Ceng , Jen‐Chih Yao

A hybrid extragradient method for approximating the common solutions of a variational inequality, a system of variational inequalities, a mixed equilibrium problem and a fixed point problem

2011-12-08
K.R. Kazmi , Shuja Haider Rizvi

An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

2020-09-10
Monairah Alansari , Mohammad Farid , Rehan Ali
Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family … Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.
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On Lipschitz-type maximal functions and their smoothness spaces

1988-01-01
Burkhard Lenze

Strong Convergence of Projected Subgradient Methods for Nonsmooth and Nonstrictly Convex Minimization

2008-10-22
Paul-Émile Maingé

Inertial Douglas–Rachford splitting for monotone inclusion problems

2015-02-12
Radu Ioan Boţ , Ernö Robert Csetnek , Christopher Hendrich
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Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications

1993-11-24
Ya. I. Alber
Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is … Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It provides an absolutely best approximation for arbitrary elements from Hilbert space by the elements of convex closed sets . This leads to a variety of applications of this operator for investigating theoretical questions in analysis and for approximation methods. Metric projection operators in Banach space do not have properties mentioned above and their applications are not straightforward. Two of the most important applications of the method of metric projection operators are as follows: 1. Solve a variational inequality by the iterative-projection method, 2. Find common point of convex sets by the iterative-projection method. In Banach space these problems can not be solved in the framework of metric projection operators. Therefore, in the present paper we introduce new generalized projection operators in Banach space as a natural generalization of metric projection operators in Hilbert space. In Sections 2 and 3 we introduce notations and recall some results from the theory of variational inequalities and theory of approximation. Then in Sections 4 and 5 we describe the properties of metric projection operators $P_\Omega$ in Hilbert and Banach spaces and also formulate equivalence theorems between variational inequalities and direct projection equations with these

A new mapping for finding common solutions of equilibrium problems and fixed point problems of finite family of nonexpansive mappings

2009-03-10
Atid Kangtunyakarn , Suthep Suantai

An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

2021-11-29
Mohammad Farid , Rehan Ali , Watcharaporn Cholamjiak
In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem … In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.
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Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals

2005-01-11
Tomonari Suzuki

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

2011-01-01
Heinz H. Bauschke , Patrick L. Combettes

Construction of a new family of Bernstein‐Kantorovich operators

2017-08-17
S. A. Mohiuddine , Tuncer Acar , Abdullah Alotaibi
In the present paper, we construct a new sequence of Bernstein‐Kantorovich operators depending on a parameter α . The uniform convergence of the operators and rate of convergence in local … In the present paper, we construct a new sequence of Bernstein‐Kantorovich operators depending on a parameter α . The uniform convergence of the operators and rate of convergence in local and global sense in terms of first‐ and second‐order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein‐Kantorovich operators and their approximation behaviors.

COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE

2016-01-01
Behzad Djafari-Rouhani , Mohammad Farid , K.R. Kazmi
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a … In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

Some methods of speeding up the convergence of iteration methods

1964-01-01
B. T. Polyak

A multiprojection algorithm using Bregman projections in a product space

1994-09-01
Yair Censor , Tommy Elfving

The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space

2010-10-14
Yair Censor , Aviv Gibali , Simeon Reich
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Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem

2011-08-30
Charles L. Byrne , Yair Censor , Aviv Gibali +1 more
We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, … We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which under a given bounded linear transformation is a zero of another maximal monotone mapping. We present three iterative algorithms that solve such problems in Hilbert

The Convex Feasibility Problem in Image Recovery

1996-01-01
Patrick L. Combettes

A strong convergence theorem for relatively nonexpansive mappings in a Banach space

2005-04-11
Shin-ya Matsushita , Wataru Takahashi

Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems

2018-02-05
Suhel Ahmad Khan , Suthep Suantai , Watcharaporn Cholamjiak

On the Existence of Solutions of Quasivariational Inclusion Problems

2004-11-05
Nguyen Xuan Tan

Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales

1922-01-01
Stefan Banach
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Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space

2004-01-01
Felipe Álvarez
This paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a Hilbert space which unifies three previously studied strategies: relaxation, inertial type extrapolation … This paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a Hilbert space which unifies three previously studied strategies: relaxation, inertial type extrapolation and projection step. The first two strategies are intended to speed up the convergence of the standard proximal point algorithm, while the third permits one to perform inexact proximal iterations with fixed relative error tolerance. The paper establishes the global convergence of the method for the weak topology under appropriate assumptions on the algorithm parameters.

A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces

2010-04-21
Narin Petrot , Kriengsak Wattanawitoon , Poom Kumam

Korovkin-type Approximation Theory and its Applications

1994-12-31
Francesco Altomare , Michele Campıtı

An extragradient-like approximation method for variational inequalities and fixed point problems

2011-07-27
Lu-Chuan Ceng , Qamrul Hasan Ansari , Ngai‐Ching Wong +1 more
Abstract The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the … Abstract The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process. We establish a strong convergence theorem for two sequences generated by this extragradient-like iterative algorithm. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings. 1991 MSC: 47H09; 47J20.
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Local approximation properties for certain King type operators

2013-01-01
Ali Özarslan , Hüseyin Aktuğlu
In this paper, we consider a certain King type operators which includes general families of Szász-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, … In this paper, we consider a certain King type operators which includes general families of Szász-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, which provides global approximation for the above mentioned operators, we obtain the rate of convergence of this class. Furthermore, we give local approximation results by using the first and the second modulus of continuity.
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Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems

2007-12-18
Xiaolong Qin , Meijuan Shang , Yongfu Su