Abstract
Given any a := (a1; a2,... ; an) and b := (b1; b2;... ; bn) in Rn. The n-fold convex function dened on [a; b], a; b 2 Rn with a < b is a convex function in each variable separately. In this work we prove an inequality of Hermite-Hadamard type for n-fold convex functions. Namely, we establish the inequality
 
Highlights
The classical Hermite-Hadamard inequality a+b b f (a) + f (b) ≤ f (t) dt ≤b−a a holds for all convex functions defined on a real interval [a, b]. (1.1)Along the past thirty years, several authors give an attention for various kind of this inequality and related type inequalities
B−a a holds for all convex functions defined on a real interval [a, b]
The history of (1.1) is very long to summarize in one or two paragraph, we can say without any worry, the real work over all these thirty years started in 1992 by Dragomir [5]
Summary
B−a a holds for all convex functions defined on a real interval [a, b]. Dragomir proved various inequalities of Hermite-Hadamard type for several assumption for the functions involved; e.g., convex mappings defined on a disk in the plane and convex mappings defined on a ball in the space . In 2009, by using of a stochastic approach, de la Cal et al established a multidimensional version of the classical HermiteHadamard inequalities which holds for convex functions on general convex bodies. In [6], Dragomir established the following similar inequality of Hadamard’s type for co–ordinated convex mapping on a rectangle from the plane R2.
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