Bo-Yan Xi

Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamards integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

On Hermite-Hadamard Type Inequalities for ( α , M )-Convex Functions

In the paper, some new inequalities of Hermite-Hadamard type for (α,m)-convex functions are obtained.

Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle

Abstract. In the paper, the authors obtain some Hermite–Hadamard type integral inequalities for extended s-convex functions on the co-ordinates in a rectangle.

HERMITE-HADAMARD TYPE INEQUALITIES FOR GEOMETRIC-ARITHMETICALLY s-CONVEX FUNCTIONS

In the paper, several properties of geometric-arithmetically s-convex functions are provided, an integral identity in which the inte- grands are products of a function and a derivative is found, and then some inequalities of Hermite-Hadamard type for integrals whose inte- grands are products of a derivative and a function whose derivative is of the geometric-arithmetic s-convexity are established.

Inequalities of Hermite-Hadamard type involving an s-convex function with applications

In the paper, the authors establish some integral inequalities of Hermite-Hadamard type involving the product of an s -convex function and a symmetric function and apply these new established inequalities to construct inequalities for special means.

Some new inequalities of Hermite–Hadamard type forn-time differentiable functions which arem-convex

Abstract In the paper, by setting up an integral identity and using Hölder integral inequality, the authors establish some new inequalities of Hermite–Hadamard type for n-time differentiable and m-convex functions and discuss applications of these inequalities to special means.

Some inequalities for (h,m)-convex functions

In the paper, the authors give some inequalities of Jensen type and Popoviciu type for (h,m)-convex functions and apply these inequalities to special means.MSC: 26A51, 26D15, 26E60.

Some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions

Abstract In the paper, the authors establish some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions of two variables.

Majorization involving the cyclic moving average

We solve an open problem on some majorization inequalities involving the cyclic moving average.

Properties and inequalities for the (h1, h2)- and (h1, h2, m)-GA-convex functions

In the paper, the authors introduce definitions of the -GA-convex functions and the -GA-convex functions, discuss some properties of these kinds of functions, establish some integral inequalities for these functions, and apply these inequalities to construct several more inequalities.