New Hermite–Hadamard Type Inequalities in Connection with Interval-Valued Generalized Harmonically (h1,h2)-Godunova–Levin Functions

Abstract

As is known, integral inequalities related to convexity have a close relationship with symmetry. In this paper, we introduce a new notion of interval-valued harmonically m,h1,h2-Godunova–Levin functions, and we establish some new Hermite–Hadamard inequalities. Moreover, we show how this new notion of interval-valued convexity has a close relationship with many existing definitions in the literature. As a result, our theory generalizes many published results. Several interesting examples are provided to illustrate our results.