The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues.The Hermite-Hadamard inequality which is also used …
The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues.The Hermite-Hadamard inequality which is also used frequently in many other parts of practical mathematics notably in optimization and probability is one of the most important mathematical inequalities relevant to convex maps.The fractional calculus, a calculus of non-integer order has applications in diverse fields of physical sciences.In this paper, we have established Hermite-Hadamard's inequalities via Riemann-Liouville fractional integral for the case of harmonically convex function as well as the products of two harmonically convex functions via Riemann-Liouville fractional integrals.
The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it …
The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it was done by F.H. Jackson in the beginning of the twentieth century. The rapid growth on q-calculus is due to its applications in various branches of mathematical and physical sciences. Of them, one of the most basic and important functions in the theory of geometric function is convexity having its wider applications in pure and applied mathematics. As it still lacks the intensive study on quantum estimates on the various types of integral inequalities, we focus our study on quantum estimates of Hermite-Hadamard type integral inequality especially on coordinated convex functions. In this paper, we have extended Hermite-Hadamard type integral inequality for coordinated convex function in terms of quantum framework.
Integral inequality is a fascinating research domain that helps to estimate the integral mean of convex functions. The convexity theory plays a basic role in the development of various branches …
Integral inequality is a fascinating research domain that helps to estimate the integral mean of convex functions. The convexity theory plays a basic role in the development of various branches of applied sciences. Convexity and inequality are connected which has a fundamental character in many branches of pure and applied disciplines. The Hermite-Hadamard (H-H) type integral inequality is one of the most important inequalities associated with the convex functions. The researchers are being motivated to the extensions, enhancements and generalizations of H-H type inequality for different types of convex functions. In this paper, we have obtained an extension of some integral inequalities of Hermite-Hadamard type for m-convex functions with second order derivatives on the basis of the classical convex functions.
Integral inequality is a fascinating research domain that helps to estimate the integral mean of convex functions. The convexity theory plays a basic role in the development of various branches …
Integral inequality is a fascinating research domain that helps to estimate the integral mean of convex functions. The convexity theory plays a basic role in the development of various branches of applied sciences. Convexity and inequality are connected which has a fundamental character in many branches of pure and applied disciplines. The Hermite-Hadamard (H-H) type integral inequality is one of the most important inequalities associated with the convex functions. The researchers are being motivated to the extensions, enhancements and generalizations of H-H type inequality for different types of convex functions. In this paper, we have obtained an extension of some integral inequalities of Hermite-Hadamard type for m-convex functions with second order derivatives on the basis of the classical convex functions.
The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it …
The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it was done by F.H. Jackson in the beginning of the twentieth century. The rapid growth on q-calculus is due to its applications in various branches of mathematical and physical sciences. Of them, one of the most basic and important functions in the theory of geometric function is convexity having its wider applications in pure and applied mathematics. As it still lacks the intensive study on quantum estimates on the various types of integral inequalities, we focus our study on quantum estimates of Hermite-Hadamard type integral inequality especially on coordinated convex functions. In this paper, we have extended Hermite-Hadamard type integral inequality for coordinated convex function in terms of quantum framework.
The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues.The Hermite-Hadamard inequality which is also used …
The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues.The Hermite-Hadamard inequality which is also used frequently in many other parts of practical mathematics notably in optimization and probability is one of the most important mathematical inequalities relevant to convex maps.The fractional calculus, a calculus of non-integer order has applications in diverse fields of physical sciences.In this paper, we have established Hermite-Hadamard's inequalities via Riemann-Liouville fractional integral for the case of harmonically convex function as well as the products of two harmonically convex functions via Riemann-Liouville fractional integrals.
The main aim of the present note is to establish new Hadmard like integral inequalities involving two log-convex functions.
The main aim of the present note is to establish new Hadmard like integral inequalities involving two log-convex functions.
We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary …
We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary and based on the use of the Minkowski, Hölder, and Young inequalities.