engleski

On h-convexity

We introduce a class of h-convex functions which generalize convex, s-convex, Godunova-Levin functions and P-functions. Namely, the h-convex function is defined as a non-negative function f:J \rightarrow R which satisfies f(ax+(1-a)y) \leq h(a)f(x)+h(1-a)f(y), where h is a non-negative function, a\in (0, 1) and x, y \in J. Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given.

convex function; P-function; Godunova-Levin function; s-convex and h-convex function

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