Studies On Integral Inequalities For Multivariate Co-ordinates Convex Functions

Convex functions are one of basic concepts in mathematics,inequalities are applied extensively in mathematical science,and inequalities for convex functions play very important roles in pure and applied mathematics.In recent decades,the theory of integral inequality for convex functions has been developed considerably.In 1881,Hermite raised the following integral inequality for convex functions.In 1893,Hadamard proved it.If f(x)is a convex function on [a,b],then We call this inequality the Hermite-Hadamard integral inequality.The Hermite-Hadamard integral inequality is an important starting point in the theory of inequalities.Currently,many mathematicians are studying it continuously and obtain plenty of new conclusions.For example,new notions of convex functions are introduced and new integral inequalities of the Hermite-Hadamard type are established.In 2001,S.S.Dragomir introduced the concept of multivariate convex functions on co-ordinates.Hereafter,many mathematicians defined many similar and related concepts and set up integral inequalities of the Hermite-Hadamard type.