Some H-Godunova–Levin Function Inequalities Using Center Radius (Cr) Order Relation

Interval analysis distinguishes between different types of order relations. As a result of these order relations, convexity and nonconvexity contribute to different kinds of inequalities. Despite this, convex theory is commonly known to rely on Godunova–Levin functions because their properties make it more efficient for determining inequality terms than convex ones. The purpose of this study is to introduce the notion of cr-h-Godunova–Levin functions by using total order relation between two intervals. Considering their properties and widespread use, center-radius order relation appears to be ideally suited for the study of inequalities. In this paper, various types of inequalities are introduced using center-radius order (cr) relation. The cr-order relation enables us firstly to derive some Hermite–Hadamard ((Formula presented.)) inequalities, and then to present Jensen-type inequality for h-Godunova–Levin interval-valued functions (GL- (Formula presented.)) using a Riemann integral operator. This kind of convexity unifies several new and well-known convex functions. Additionally, the study includes useful examples to support its findings. These results confirm that this new concept is useful for addressing a wide range of inequalities. We hope that our results will encourage future research into fractional versions of these inequalities and optimization problems associated with them.