Hermite–Hadamard and Jensen-Type Inequalities for Harmonical (h1, h2)-Godunova–Levin Interval-Valued Functions

Abstract

There is no doubt that convex and non-convex functions have a significant impact on optimization. Due to its behavior, convexity also plays a crucial role in the discussion of inequalities. The principles of convexity and symmetry go hand-in-hand. With a growing connection between the two in recent years, we can learn from one and apply it to the other. There have been significant studies on the generalization of Godunova–Levin interval-valued functions in the last few decades, as it has tremendous applications in both pure and applied mathematics. In this paper, we introduce the notion of interval- valued harmonical (h1, h2)-Godunova–Levin functions. Using the new concept, we establish a new interval Hermite–Hadamard and Jensen-type inequalities that generalize the ones that exist in the literature. Additionally, we provide some examples to prove the validity of our main results.