Abstract
One of the many techniques to obtain a new convex function from the given functions is to calculate the product of these functions by imposing certain conditions on the functions. In general, the product of two or finite number of convex function needs not to be convex and, therefore, leads us to the study of product of these functions. In this paper, we reframe the idea of product of functions in the setting of generalized convex function to establish Hermite–Hadamard-type inequalities for these functions. We have analyzed different cases of double and triple integrals to derive some new results. The presented results can be viewed as the refinement and improvement of previously known results.
Highlights
Convexity has been generalized in many aspects, and the classical Hermite–Hadamard inequality is viewed by these generalizations
We study different cases of double and triple integrals to derive some new results. is is the novel and innovative approach to Journal of Mathematics characterize the convex function with the product of h−convex, m−convex, (s, m)−convex, and (α, s)−convex functions
We utilize the product of functions to develop the class of generalized convex functions using two given functions
Summary
Convexity has been generalized in many aspects, and the classical Hermite–Hadamard inequality is viewed by these generalizations. One of the very fundamental results regarding convexity is the wellreputed Hermite–Hadamard inequality. In [1], Toader extended the idea of convexity by giving the definition of an m-convex function and constructed few results including Hermite–Hadamard-type inequalities. In [22], Pachpatte investigated the product of functions for developing Hermite–Hadamard-type inequalities by using the usual convexity.
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