Hermite–Hadamard-Type Inequalities for Product of Functions by Using Convex Functions

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.