Hermite–Hadamard-Mercer Type Inequalities for Interval-Valued Coordinated Convex Functions

Determining the Jensen–Mercer inequality for interval-valued coordinated convex functions has been a challenging task for researchers in the fields of inequalities and interval analysis. We use ⊖g to establish the Jensen–Mercer inequality for interval-valued coordinated convex functions. In this paper, we make significant strides in establishing new results by introducing a novel approach. We present a Hermite–Hadamard (H.H.) Mercer-type inequality for interval-valued coordinated convex functions and show how it generalizes the traditional H.H. inequality. Specifically, the H.H. inequality for interval-valued coordinated convex functions can be derived as a special case by considering the endpoints of the H.H. Mercer-type inequality. Furthermore, we provide computational results that verify the accuracy of recent findings in the literature. Our results indicate that the proposed new results impose highly effective constraints on integrals of the specified functions and are valid for a broader class of functions. These new findings have significant implications for applications in fields such as economics, engineering, and physics, where they can improve the precision of system modeling and optimization.