Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

Abstract

Abstract In this paper, we give and study the concept of n-polynomial ( s , m ) $(s,m)$ -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial ( s , m ) $(s,m)$ -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial ( s , m ) $(s,m)$ -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

Keywords

• Hermite–Hadamard inequality
• Hölder inequality
• Power mean inequality
• ( s , m ) $(s,m)$ -exponential-type convexity
• n-polynomial