engleski

Companion inequalities to Jensen's inequality for m-convex and (alpha, m)-convex functions

General companion inequalities related to Jensen's inequality for the classes of m-convex and (alpha, m)-convex functions are presented. We show how Jensen's inequality for these two classes, as well as Slater's inequality, can be obtained from these general companion inequalities as special cases. We also present several variants of the converse Jensen's inequality, weighted Hermit-Hadamard's inequalities and inequalities of Giaccardi and Petrović for these two classes of functions.

m-convex functions; (alpha; m)-convex functions; Jensen's inequality; Slater's inequality; Hermite-Hadamard's inequalities; Giaccardi's inequality; Fejér's inequalities

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