Mappings Connected with Hermite-Hadamard Inequalities for Superquadratic Functions

Abstract

Abstract. Using some characterizations of superquadratic functions we obtain some results on two mappings H and F connected with Hermite-Hadamard inequality. Our results generalize corresponding results for convex functions. Especially, when the superquadratic function is convex at the same time, then our results represent also the refinements of those results. (2000): 26D15. Mathematics subject classification

Generalization of the Fejér-Hadamard's Inequality for Convex Function on Coordinates

“…In many areas of analysis, application of the Hadamard inequality appear for different classes of functions (see [1,3,6,10,18] for convex functions). Some useful mappings connected to this inequality are also defined by many authors, for example, see [2,5,10,14]. In recent years, the concept of convexity has been extended and generalized in various directions.…”