Int. Journal of Math. Analysis, Vol. 4, 2010, no. 30, 1473 - 1482
On Some Inequalities for h-Convex Functions M. A. Latif Aeronautical Training Center General Authority of Civil Aviation P.O. Box 15441, Jeddah 21444, Saudi Arabia m amer
[email protected]
Abstract. In this paper some inequalities for h-convex functions are established. Mathematics Suject Classification: Primary 26D15; Secondary 26A51 Keywords: convex functions, h-convex functions, s-convex functions 1. Introduction
In [7, p.6], Via Titu Andreescu established the following inequality for convex functions: Theorem 1. [7, p.6] If f is a convex function and x1 , x2 , x3 lie in its domain, then x1 + x2 + x3 (1.1) f (x1 ) + f (x2 ) + f (x3 ) + f 3 4 x1 + x2 x2 + x3 x3 + x1 ≥ f +f +f 3 2 2 2 In [10], Popoviciu proved the following inequalities for convex functions: Theorem 2. [10] If f is convex function on I and x1 , x2 , ..., xn ∈ I, then n x1 + x2 + ... + xn 2 n xi + xj (1.2) f ≥ f (xi ) + f n − 2 n n − 2 2 i=1 i
