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

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.