Journal of Mathematical Inequalities Volume 8, Number 2 (2014), 349–358

 doi:10.7153/jmi-08-25

SCHUR–CONVEXITY, SCHUR GEOMETRIC AND SCHUR HARMONIC CONVEXITIES OF DUAL FORM OF A CLASS SYMMETRIC FUNCTIONS 

HUAN-NAN SHI AND JING ZHANG

Abstract：By the properties of Schur-convex function, Schur geometrically convex function and
Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application,
several inequalities are obtained, some of which extend the known ones.

Mathematics subject classification (2010): 26D15, 05E05, 26B25.

Keywords and phrases: Schur-convexity, Schur geometric convexity, Schur harmonic convexity, inequality, log-convex function, symmetric functions, dual form.

Schur-convexity, Schur geometric and Schur harmonic convexities of dual form of .pdf

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