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, â¦, ir are non-negative integers, and p â 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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