On Generalized Hermite Hadamard’s Inequality

Abstract

The object is to construct the log-convex and the exponential convex functions via functional generalization of Hermite Hadamard’s inequality for some special classes of continuous functions defined on compact interval in R. Constructed n-exponentially convex functions are used to obtain the generalization of already discovered mean with positive weights p and q, and prove their monotonicity
and also introduce several classes of Stolarsky means called Stolarsky type means. Prove Minkowsky type inequalities for new discovered means as applications of Lyponuve type inequalities of constructed log-convex functions.

Key words and phrases. Hermite Hadamard’s inequality, log-convex function, exponential convexity.

2000 Mathematics Subject Classification. 26D15, 26D99