Hermite Hadamard type inequalities for product of log convex function and exponential convex functions and some generalized results

Abstract

In this article, the author explores and establishes results related to Hermite-Hadamard type inequalities specifically for log-convex and exponentially convex functions. The study focuses on deriving and proving these inequalities, which provide bounds on the integral mean of a function in terms of its values at specific points. Additionally, the author extends these fundamental results by presenting generalized versions of the inequalities. This generalization is supported by concrete examples that illustrate how the inequalities apply in different cases. These examples help demonstrate the practical implications and validity of the derived inequalities in mathematical analysis and related fields.