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

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

doi:10.59400/jam2388

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

Huan-Nan Shi Department of Electronic Information, Teacher’s College, Beijing Union University, Beijing 100011, China
Jing Zhang Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China
Wei-Shih Du Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan

Article ID: 2388

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

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.

References

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[3]Shi HN, Zhang J, Ma QH. Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function. SpringerPlus. 2016; 5: 296.

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[7]Zhang XM. Geometrically Convex Functions (Chinese). Anhui University Press; 2004.

[8]Chu YM, Zhang X, Wang G. The Schur geometrical convexity of the extended mean values. Journal of Convex Analysis. 2008; 15(4): 707–718.

[9]Chu YM, Lv YP. The Schur harmonic convexity of the Hamy symmetric function and its applications. Journal of Inequalities and Applications. 2009. doi: 10.1155/2009/838529

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Published

2025-03-05

How to Cite

Shi, H.-N., Zhang, J., & Du, W.-S. (2025). A note on Schur convexity for compositions of complete symmetric functions and new simple proofs. Journal of AppliedMath, 3(1), 2388. https://doi.org/10.59400/jam2388

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