Jensen and Hermite-Hadamard type inclusions for harmonical $ h $-Godunova-Levin functions

Abstract

<abstract><p>The role of integral inequalities can be seen in both applied and theoretical mathematics fields. According to the definition of convexity, it is possible to relate both concepts of convexity and integral inequality. Furthermore, convexity plays a key role in the topic of inclusions as a result of its definitional behavior. The importance and superior applications of convex functions are well known, particularly in the areas of integration, variational inequality, and optimization. In this paper, various types of inequalities are introduced using inclusion relations. The inclusion relation enables us firstly to derive some Hermite-Hadamard inequalities (H.H-inequalities) and then to present Jensen inequality for harmonical $ h $-Godunova-Levin interval-valued functions (GL-IVFS) via Riemann integral operator. Moreover, the findings presented in this study have been verified with the use of useful examples that are not trivial.</p></abstract>