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Niculescu C.P., Convexity according to the geometric mean, Math. Inequal. Appl., 2000, 2, 155-167.

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Article

Schur m-Power Convexity of a New Class of Symmetric Functions with Applications

1College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, China


Turkish Journal of Analysis and Number Theory. 2021, Vol. 9 No. 3, 42-47
DOI: 10.12691/tjant-9-3-2
Copyright © 2021 Science and Education Publishing

Cite this paper:
Shuhong Wang, Hui Wang, Haiyan Yu. Schur m-Power Convexity of a New Class of Symmetric Functions with Applications. Turkish Journal of Analysis and Number Theory. 2021; 9(3):42-47. doi: 10.12691/tjant-9-3-2.

Correspondence to: Shuhong  Wang, College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, China. Email: shuhong7682@163.com

Abstract

In the paper, by using the properties of Schur m-power convex function, we discuss Schur m-power convexity of a new class of symmetric functions where i1, i2, …, ir are non-negative integers, and p ∈ N+. We obtain that is Schur m-power convex for m ≤ 0 and Schur m-power concave for m ≥ p. We also give a counter example to illustrate is neither Schur convex nor Schur concave for p>1. As applications, a Klamkin-Newman type inequality and some analytic inequalities are derived.

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