Some Integral Inequalities Involving Exponential Type Convex Functions and Applications

Abstract

In this present case, we focus and explore the idea of a new family of convex function namely exponential
type m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraic
properties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.
Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.
Further, in the manner of this newly introduced idea, we investigate some applications of special
means. These new results yield us some generalizations of the prior results in the literature. We believe, the
methodology investigated in this paper will further inspire intrigued researchers.