eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2021-11-12 9 3 42 47 10.12691/tjant-9-3-2 TJANT2021932 article Shuhong Wang shuhong7682@163.com 1 Hui Wang 1 Haiyan Yu 1 College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, China 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 ¡Ê N+. We obtain that is Schur m-power convex for m ¡Ü 0 and Schur m-power concave for m ¡Ý 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. http://pubs.sciepub.com/tjant/9/3/2/tjant-9-3-2.pdf Schurm-power convexity symmetric function mean majorization inequality