Journal of Mathematical Sciences: Advances and Applications

Volume 66, 2021, Pages 1-19

Available at http://scientificadvances.co.in

DOI: http://dx.doi.org/10.18642/jmsaa_7100122195

SCHUR-CONVEXITY OF A CLASS OF 

ELEMENTARY SYMMETRIC COMPOSITE FUNCTIONS

HUAN-NAN SHI1, TAO ZHANG  and BO-YAN XI

Abstract：In this paper, using the properties of Schur-convex function, Schurgeometrically

convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity on   and Schur-harmonic convexity on for a composite function of the elementary symmetric functions.

Keywords and phrases: Schur-convesxity, Schur-geometric convexity, Schur-harmonic

convexity, elementary symmetric function.

2020 Mathematics Subject Classification: 26E60, 26D16, 26A51.

Schur-convexity of a class of elementary symmetric composite functions（Shi-Zhang-Xi).pdf