For x = (x 1, x 2, …, x n ) ∈ (0, 1 ]n and r ∈ { 1, 2, … , n}, a symmetric function F n (x, r) is defined by the relation
where i 1, i 2 ,… , i n are positive integers. This paper deals with the Schur convexity and Schur multiplicative convexity of F n (x, r). As applications, some inequalities are established by using the theory of majorization.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 10, pp. 1306–1318, October, 2009.
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Xia, WF., Chu, YM. Schur convexity and Schur multiplicative convexity for a class of symmetric functions with applications. Ukr Math J 61, 1541–1555 (2009). https://doi.org/10.1007/s11253-010-0296-8
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DOI: https://doi.org/10.1007/s11253-010-0296-8