Some new generalizations of integral inequalities for harmonical cr-(h(1),h(2))-Godunova-Levin functions and applications

Abstract

The interval analysis is famous for its ability to deal with uncertain data. This method is useful for addressing models with data that contain inaccuracies. Different concepts are used to handle data uncertainty in an interval analysis, including a pseudo-order relation, inclusion relation, and center–radius (cr)-order relation. This study aims to establish a connection between inequalities and a cr-order relation. In this article, we developed the Hermite–Hadamard (H.H) and Jensen-type inequalities using the notion of harmonical (h1, h2)-Godunova–Levin (GL) functions via a cr-order relation which is very novel in the literature. These new definitions have allowed us to identify many classical and novel special cases that illustrate our main findings. It is possible to unify a large number of well-known convex functions using the principle of this type of convexity. Furthermore, for the sake of checking the validity of our main findings, some nontrivial examples are given.