Huan-Nan Shi

Schur Convexity of Generalized Heronian Means Involving Two Parameters

The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.

Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions

The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions are given. As their application, some analytic inequalities are established.MSC:26D15, 05E05, 26B25.

Two double inequalities for k-gamma and k-Riemann zeta functions

By using methods in the theory of majorization, a double inequality for the gamma function is extended to the k-gamma function and the k-Riemann zeta function.MSC:33B15, 26D07, 26B25.

Schur-convexity of dual form of some symmetric functions

By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric functions is simply proved.MSC:26D15, 05E05, 26B25.

A relation of weak majorization and its applications to certain inequalities for means

A relation of weak majorization for n-dimensional real vectors is established, the result is then used to derive some inequalities involving the power mean, the arithmetic mean and the geometric mean in n variables.

Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities

In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.

New proofs of Schur-concavity for a class of symmetric functions

By properties of the Schur-convex function, Schur-concavity for a class of symmetric functions is simply proved uniform.2000 Mathematics Subject Classification: Primary 26D15; 05E05; 26B25.

Refinements of Inequalities among Difference of Means

In this paper, for the difference of famous means discussed by Taneja in 2005, we study the Schur-geometric convexity in (0, ∞) × (0, ∞) of the difference between them. Moreover some inequalities related to the difference of those means are obtained.

Majorization involving the cyclic moving average

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