In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived âŚ
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces.
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. âŚ
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous âŚ
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms.As an application, a partial answer to Kirk's problem in metric spaces is given.
In this article, we attempt to provide a more general method based on Petryshynâs fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations âŚ
In this article, we attempt to provide a more general method based on Petryshynâs fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C ( I ). Some results regarding the existence of fixed points in implicit functional integral equations will be reviewed in the literature. We show that this general result unifies and improves many of the main results in the literature. To illustrate that our approach is more general than other methods, we present some concrete examples. Also, we apply our method to create new functional equations in practice and check the existence of solutions.
In this study, a fuzzy Meir-Keelerâs contraction theorem for complete FMS based on George and Veeramani idea is established. Then, we characterize fuzzy Meir-Keelerâs contractions as contractive types induced by âŚ
In this study, a fuzzy Meir-Keelerâs contraction theorem for complete FMS based on George and Veeramani idea is established. Then, we characterize fuzzy Meir-Keelerâs contractions as contractive types induced by functions called fuzzy <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>L</mi> </math> -function. Moreover, we show that the converse of it is true. Finally, we bring some examples and corollaries certify our results and new improvement.
In this study, an efficient iterative numerical technique based on quadrature formula is proposed to solve nonlinear (mixed) Volterra and Fredholm integral equations of the second kind in any dimension. âŚ
In this study, an efficient iterative numerical technique based on quadrature formula is proposed to solve nonlinear (mixed) Volterra and Fredholm integral equations of the second kind in any dimension. Also, we obtain the error estimation of the iterative method in terms of the modulus of continuity. Furthermore, some numerical examples are considered to confirm the applicability of the method.
In this paper, we show that recent numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto. âAn existence result with numerical solution of nonlinear fractional integral equations.â Mathematical Methods âŚ
In this paper, we show that recent numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto. âAn existence result with numerical solution of nonlinear fractional integral equations.â Mathematical Methods in the Applied Sciences (2023)] is wrong. The method was modified and developed. With an example, it can be seen that using the midpoint rule will not be suitable, instead using Jacobiâs quadrature rule can work well. MSC: 60H20, 47H10.
In this article, we attempt to provide a more general method based on Petryshyn's fixed point theorem to ensure the existence of solutions to implicit functional equations.These implicit functional equations âŚ
In this article, we attempt to provide a more general method based on Petryshyn's fixed point theorem to ensure the existence of solutions to implicit functional equations.These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C(I).Some results regarding the existence of fixed point in implicit functional integral equations will be reviewed in the literature.We show that this general result unifies and improves many main results in the literature.To illustrate that our approach is more general than other methods, we present some concrete examples.Also, we apply our method to create new functional equation in practice and check the existence of solution.MSC: 31B10, 47H10, 47H08, 60H20.
The recent iterative numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto, "An existence result with numerical solution of nonlinear fractional integral equations," Mathematical Methods in the Applied Sciences âŚ
The recent iterative numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto, "An existence result with numerical solution of nonlinear fractional integral equations," Mathematical Methods in the Applied Sciences ( 2023)] requires some corrections, as we point out in this note.We give a counterexample to one of their main statements (Theorem 5.1).The iterative method used is untrue, and we will correct it.With an example, it can be seen that using the midpoint rule will not be suitable and accurate in fractional cases (0 < Ď < 1); instead, using Jacobi's quadrature rule can work well.Also, to show the validity of our numerical method, a non-linear example is considered.MSC: 60H20, 47H10.
In this paper, using the technique of measures of noncompactness, we employ the Petryshynâs fixed point theorem as a generalization of classical Schauder fixed point principle to investigate the solution âŚ
In this paper, using the technique of measures of noncompactness, we employ the Petryshynâs fixed point theorem as a generalization of classical Schauder fixed point principle to investigate the solution of some general nonlinear fractional integral equations in the Banach space of continuous functions . Also, for applicability of the obtained results of our theorem, some examples are given.
This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak Îś-contractions under weaker conditions. The Banach contraction âŚ
This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak Îś-contractions under weaker conditions. The Banach contraction principle is extended using the Kummer test, which generalizes this principle to weak Îś-contractions, providing error estimates for various types of contractions, including Boyd and Wong's contraction. The results not only offer new findings but also improve and complete several earlier works. Additionally, practical examples are provided to illustrate the applications and demonstrate the necessity of certain assumptions in the theory of metric fixed points.
This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak Îś-contractions under weaker conditions. The Banach contraction âŚ
This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak Îś-contractions under weaker conditions. The Banach contraction principle is extended using the Kummer test, which generalizes this principle to weak Îś-contractions, providing error estimates for various types of contractions, including Boyd and Wong's contraction. The results not only offer new findings but also improve and complete several earlier works. Additionally, practical examples are provided to illustrate the applications and demonstrate the necessity of certain assumptions in the theory of metric fixed points.
In this paper, using the technique of measures of noncompactness, we employ the Petryshynâs fixed point theorem as a generalization of classical Schauder fixed point principle to investigate the solution âŚ
In this paper, using the technique of measures of noncompactness, we employ the Petryshynâs fixed point theorem as a generalization of classical Schauder fixed point principle to investigate the solution of some general nonlinear fractional integral equations in the Banach space of continuous functions . Also, for applicability of the obtained results of our theorem, some examples are given.
The recent iterative numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto, "An existence result with numerical solution of nonlinear fractional integral equations," Mathematical Methods in the Applied Sciences âŚ
The recent iterative numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto, "An existence result with numerical solution of nonlinear fractional integral equations," Mathematical Methods in the Applied Sciences ( 2023)] requires some corrections, as we point out in this note.We give a counterexample to one of their main statements (Theorem 5.1).The iterative method used is untrue, and we will correct it.With an example, it can be seen that using the midpoint rule will not be suitable and accurate in fractional cases (0 < Ď < 1); instead, using Jacobi's quadrature rule can work well.Also, to show the validity of our numerical method, a non-linear example is considered.MSC: 60H20, 47H10.
In this article, we attempt to provide a more general method based on Petryshynâs fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations âŚ
In this article, we attempt to provide a more general method based on Petryshynâs fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C ( I ). Some results regarding the existence of fixed points in implicit functional integral equations will be reviewed in the literature. We show that this general result unifies and improves many of the main results in the literature. To illustrate that our approach is more general than other methods, we present some concrete examples. Also, we apply our method to create new functional equations in practice and check the existence of solutions.
In this article, we attempt to provide a more general method based on Petryshyn's fixed point theorem to ensure the existence of solutions to implicit functional equations.These implicit functional equations âŚ
In this article, we attempt to provide a more general method based on Petryshyn's fixed point theorem to ensure the existence of solutions to implicit functional equations.These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C(I).Some results regarding the existence of fixed point in implicit functional integral equations will be reviewed in the literature.We show that this general result unifies and improves many main results in the literature.To illustrate that our approach is more general than other methods, we present some concrete examples.Also, we apply our method to create new functional equation in practice and check the existence of solution.MSC: 31B10, 47H10, 47H08, 60H20.
In this paper, we show that recent numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto. âAn existence result with numerical solution of nonlinear fractional integral equations.â Mathematical Methods âŚ
In this paper, we show that recent numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto. âAn existence result with numerical solution of nonlinear fractional integral equations.â Mathematical Methods in the Applied Sciences (2023)] is wrong. The method was modified and developed. With an example, it can be seen that using the midpoint rule will not be suitable, instead using Jacobiâs quadrature rule can work well. MSC: 60H20, 47H10.
In this study, an efficient iterative numerical technique based on quadrature formula is proposed to solve nonlinear (mixed) Volterra and Fredholm integral equations of the second kind in any dimension. âŚ
In this study, an efficient iterative numerical technique based on quadrature formula is proposed to solve nonlinear (mixed) Volterra and Fredholm integral equations of the second kind in any dimension. Also, we obtain the error estimation of the iterative method in terms of the modulus of continuity. Furthermore, some numerical examples are considered to confirm the applicability of the method.
In this study, a fuzzy Meir-Keelerâs contraction theorem for complete FMS based on George and Veeramani idea is established. Then, we characterize fuzzy Meir-Keelerâs contractions as contractive types induced by âŚ
In this study, a fuzzy Meir-Keelerâs contraction theorem for complete FMS based on George and Veeramani idea is established. Then, we characterize fuzzy Meir-Keelerâs contractions as contractive types induced by functions called fuzzy <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>L</mi> </math> -function. Moreover, we show that the converse of it is true. Finally, we bring some examples and corollaries certify our results and new improvement.
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous âŚ
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms.As an application, a partial answer to Kirk's problem in metric spaces is given.
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. âŚ
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived âŚ
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces.
The adjective seems to be a very popular and very frequent one in the contemporary studies concerning the logical and set-theoretical foundations of mathematics. The main reason of this quick âŚ
The adjective seems to be a very popular and very frequent one in the contemporary studies concerning the logical and set-theoretical foundations of mathematics. The main reason of this quick development is, in our opinion, easy to be understood. The surrounding us world is full of uncertainty, the information we obtain from the environment, the notions we use and the data resulting from our observation or measurement are, in general, vague and incorrect. So every formal description of the real world or some of its aspects is, in every case, only an approxima tion and an idealization of the actual state. The notions like fuzzy sets, fuzzy orderings, fuzzy languages etc. enable to handle and to study the degree of uncertainty mentioned above in a purely mathematic and formal way. A very brief survey of the most interest ing results and applications concerning the notion of fuzzy set and the related ones can be found in [l]. The aim of this paper is to apply the concept of fuzziness to the clasical notions of metric and metric spaces and to compare the obtained notions with those resulting from some other, namely probabilistic statistical, generalizations of metric spaces. Our aim is to write this paper on a quite self-explanatory level the references being necessary only for the reader wanting to study these matters in more details.
Let <italic>X</italic> be a normed linear space and let <italic>K</italic> be a convex subset of <italic>X</italic>. The inward set, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper K Baseline left-parenthesis âŚ
Let <italic>X</italic> be a normed linear space and let <italic>K</italic> be a convex subset of <italic>X</italic>. The inward set, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper K Baseline left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{I_K}(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, of <italic>x</italic> relative to <italic>K</italic> is defined as follows: <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper K Baseline left-parenthesis x right-parenthesis equals left-brace x plus c left-parenthesis u minus x right-parenthesis colon c greater-than-or-slanted-equals 1 comma u element-of upper K right-brace"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>c</mml:mi> <mml:mo>⊞<!-- ⊞ --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mi>K</mml:mi> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{I_K}(x) = \{ x + c(u - x):c \geqslant 1,u \in K\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. A mapping <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T colon upper K right-arrow upper X"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>:</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy="false">â<!-- â --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">T:K \to X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is said to be inward if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T x element-of upper I Subscript upper K Baseline left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mi>x</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">Tx \in {I_K}(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for each <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x element-of upper K"> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">x \in K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and weakly inward if <italic>Tx</italic> belongs to the closure of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper K Baseline left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{I_K}(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for each <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x element-of upper K"> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">x \in K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this paper a characterization of weakly inward mappings is given in terms of a condition arising in the study of ordinary differential equations. A general fixed point theorem is proved and applied to derive a generalization of the Contraction Mapping Principle in a complete metric space, and then applied together with the characterization of weakly inward mappings to obtain some fixed point theorems in Banach spaces.
In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in âŚ
In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. âŚ
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A.George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems
We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given âŚ
We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived âŚ
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces.The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces.
By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional âŚ
By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional integral equations that arise in various branches of mathematical analysis and their applications. Also, the numerical iterative method is employed successfully to find the solutions to fractional integral equations. Lastly, we recall some different cases and examples to verify the applicability of our study.
Preface Notation Preliminaries Notation and Definitions Orthogonal Polynomials Finite and Divided Differences Interpolation Semi-Infinite Interval Convergence Accelerators Polynomial Splines Interpolatory Quadrature Riemann Integration Euler-Maclaurin Expansion Interpolatory Quadrature Rules Newton-Cotes Formulas âŚ
Preface Notation Preliminaries Notation and Definitions Orthogonal Polynomials Finite and Divided Differences Interpolation Semi-Infinite Interval Convergence Accelerators Polynomial Splines Interpolatory Quadrature Riemann Integration Euler-Maclaurin Expansion Interpolatory Quadrature Rules Newton-Cotes Formulas Basic Quadrature Rules Repeated Quadrature Rules Romberg's Scheme Gregory's Correction Scheme Interpolatory Product Integration Iterative and Adaptive Schemes Test Integrals Gaussian Quadrature Gaussian Rules Extended Gaussian Rules Other Extended Rules Analytic Functions Bessel's Rule Gaussian Rules for the Moments Finite Oscillatory Integrals Noninterpolatory Product Integration Test Integrals Improper Integrals Infinite Range Integrals Improper Integrals Slowly Convergent Integrals Oscillatory Integrals Product Integration Singular Integrals Quadrature Rules Product Integration Acceleration Methods Singular and Hypersingular Integrals Computer-Aided Derivations Fourier Integrals and Transforms Fourier Transforms Interpolatory Rules for Fourier Integrals Interpolatory Rules by Rational Functions Trigonometric Integrals Finite Fourier Transforms Discrete Fourier Transforms Hartley Transform Inversion of Laplace Transforms Use of Orthogonal Polynomials Interpolatory Methods Use of Gaussian Quadrature Rules Use of Fourier Series Use of Bromwich Contours Inversion by the Riemann Sum New Exact Laplace Inverse Transforms Wavelets Orthogonal Systems Trigonometric System Haar System Other Wavelet Systems Daubechies' System Fast Daubechies Transforms Integral Equations Nystrom System Integral Equations of the First Kind Integral Equations of the Second Kind Singular Integral Equations Weakly Singular Equations Cauchy Singular Equations of the First Kind Cauchy Singular Equations of the Second Kind Canonical Equation Finite-Part Singular Equations Integral Equations Over a Contour Appendix A: Quadrature Tables Cotesian Numbers, Tabulated for kGBPn/2, n=1(1)11 Weights for a Single Trapezoidal Rule and Repeated Simpson's Rule Weights for Repeated Simpson's Rule and a Single Trapezoidal Rule Weights for a Single 3/8-Rule and Repeated Simpson's Rule Weights for Repeated Simpson's Rule and a Single 3/8-Rule Gauss-Legendre Quadrature Gauss-Laguerre Quadrature Gauss-Hermite Quadrature Gauss-Radau Quadrature Gauss-Lobatto Quadrature Nodes of Equal-Weight Chebyshev Rule Gauss-Log Quadrature Gauss-Kronrod Quadrature Rule Patterson's Quadrature Rule Filon's Quadrature Formula Gauss-Cos Quadrature on [pi/2, pi/2] Gauss-Cos Quadrature on [0, pi/2] Coefficients in (5.1.15) with w(x)=ln(1/x), 0
A numerical method for solving nonlinear Fredholm integral equations, based on the Haar wavelet approach, is presented.Its efficiency is tested by solving four examples for which the exact solution is âŚ
A numerical method for solving nonlinear Fredholm integral equations, based on the Haar wavelet approach, is presented.Its efficiency is tested by solving four examples for which the exact solution is known.This allows us to estimate the exactness of the obtained numerical results.High accuracy of the results even in the case of a small number of grid points is observed.
Journal Article An Euler-type method for two-dimensional Volterra integral equations of the first kind Get access S McKee, S McKee Search for other works by this author on: Oxford Academic âŚ
Journal Article An Euler-type method for two-dimensional Volterra integral equations of the first kind Get access S McKee, S McKee Search for other works by this author on: Oxford Academic Google Scholar T Tang, T Tang Search for other works by this author on: Oxford Academic Google Scholar T Diogo T Diogo Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Numerical Analysis, Volume 20, Issue 3, July 2000, Pages 423â440, https://doi.org/10.1093/imanum/20.3.423 Published: 01 July 2000
The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In âŚ
The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we in- vestigate the set of all t-best approximations to an element from a set.
In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric âŚ
In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.
Abstract In this manuscript we introduce the notions of R -function and R -contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of âŚ
Abstract In this manuscript we introduce the notions of R -function and R -contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of contractions properly includes the family of all Meir-Keeler contractions and other well-known classes of contractions that have been given very recently (for instance, those using simulation functions and manageable functions). As a consequence, our approach turns out to be appropriate to unify the treatment of different kinds of contractive nonlinear operators.
Consider the nonlinear operator equation $x = {\mathcal {K}}(x)$ with $\mathcal {K}$ a completely continuous mapping of a domain in the Banach space $\mathcal {X}$ into $\mathcal {X}$ and let âŚ
Consider the nonlinear operator equation $x = {\mathcal {K}}(x)$ with $\mathcal {K}$ a completely continuous mapping of a domain in the Banach space $\mathcal {X}$ into $\mathcal {X}$ and let $x^ * $ denote an isolated fixed point of $\mathcal {K}$. Let $\mathcal {K}_n $, $n \geqq 1$ denote a sequence of finite dimensional approximating subspaces, and let $P_n $, be a projection of $\mathcal {X}$ onto $\mathcal {X}_n $ The projection method for solving $x = {\mathcal {K}}(x)$ given by$x_n = P_n \mathcal {K}(x_n )$, and the iterated projection solution is defined as $\tilde{x}_n = \mathcal {K}(x_n )$. We analyze the convergence of $x_n $ and $\tilde x_n $ to $x^ * $, giving a general analysis that includes both the Galerkin and collocation methods. A more detailed analysis is then given for a large class of Urysohn integral operators in one variable, showing the superconvergence of $\tilde x_n $ to $x^ * $.
We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the âŚ
We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.
Abstract A fixed point theorem is proved. Moreover, fuzzy Edelstein's contraction theorem is described. Finally, the existence of at least one periodic point is shown.
Abstract A fixed point theorem is proved. Moreover, fuzzy Edelstein's contraction theorem is described. Finally, the existence of at least one periodic point is shown.