A new Version of Jensen's Mercer Inequality and Related Inequalities of Hermite--Hadamard Type for Interval-Valued Coordinated Convex Functions

Abstract In this article, we give Jensen Mercer Inequality for interval-valuedco-ordinated convex functions because this inequality was a challenging problem forresearchers working in the field of inequalities and set valued functions. By use of this new inequality, we establish Hermite--Hadamard-Mercer type inequalities for interval-valuedco-ordinated convex functions. These newly established inequalities forinterval-valued functions are the generalization of the existing Hermite-Hadamardinequalities. Moreover, we give numericalexamples to check the validity of newly established results. The results ofthe study shows that the inequalities hold for a wider range of functionsand provide very efficient bounds on the integrals of given functions. Theuse of new results can improve the accuracy of modelling and optimization ofsystems in the fields such as economics, engineering, and physics. Mathematics Subject Classification: 26D10, 26D15, 26A51