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

Shuhong Wang^1, , Hui Wang¹ and Haiyan Yu¹

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

Cite this paper:
Shuhong Wang, Hui Wang and 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

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, …, i_r 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.

Keywords:
Schurm-power convexity symmetric function mean majorization inequality

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