Journal of Applied Math, 2025，3(1), 2388. https://doi.org/10.59400/jam2388

A note on Schur convexity for compositions of complete symmetric functionsand new simple proofs

Huan-Nan Shi, Jing Zhang, Wei-Shih Du

Abstract. In this work, by applying the properties of Schur-convex functions, Schur-geometrically convex functions and Schur-harmonically convex functions directly, we will provide more direct and simple proofs for compositions of complete symmetric functions.

2010 Mathematics Subject Classification: Primary 05E05, 26B25.

Keywords: complete symmetric function; Schur-convexity; Schur-geometric convexity; Schur-harmonic convexity; composite function

A note on Schur convexity for compositions of complete symmetric functions and n.pdf