Hermite-Hadamard Inequalities for Exponential Convexity with Applications

Abstract

This paper presents a comprehensive analysis of $(s,m)$-exponential-type functions which are convex, emphasizing their foundational algebraic properties. Building upon this framework, we drive class of latest results of Hermite-Hadamard-type inequalities by using Caputo-Fabrizio fractional integral operator. This study introduces improved integral inequalities for functions exhibiting $(s,m)$-exponential convexity in their powered absolute derivatives. The efficacy of these results is demonstrated through refined estimations of special means and tighter error bounds in trapezoidal and midpoint integration schemes.