Some characterizations of h-convex functions

Abstract

In this paper, we give some characterizations of h -convex functions, and some applications related to these functions are also obtained. According to these results, we can know better the relation between convex functions and h -convex functions.

Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$

“…Lots of properties and applications of them can be found in literatures, see e.g. [4,8,11,13,15,19,20,25]. In particular, if f satisfies (1.2) with h(t) = t, h(t) = t s (s ∈ (0, 1)), h(t) ≡ 1 and h(t) = 1/t (0 < t < 1), then f is said to be a p-convex function, (p, s)-convex function (in the second sense), (p, P )function and a p-Godunova-Levin function, respectively.…”

COMPLEMENTARY RESULTS FOR h -CONVEX FUNCTIONS WITH APPLICATIONS

“…Recently, in [10], Jin et al gave other characterizations of h-convex functions and provided some basic applications.…”