Hermite-Hadamard type inequalities via new exponential type convexity and their applications

Abstract

In this paper, authors study the concept of (s,m)-exponential type convex
functions and their algebraic properties. New generalizations of Hermite-Hadamard type inequality for the (s,m)-exponential type convex function $\psi$ and for the products of two (s,m)-exponential type convex functions $\psi$ and $\phi$ are proved. Some refinements of the (H-H) inequality for functions whose first derivative in absolute value at certain power are (s,m)-exponential type convex are obtain. Finally, many new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well.