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The Schur multiplicative and harmonic convexities of the complete symmetric function
Author(s) -
Chu Y.M.,
Wang G.D.,
Zhang X.H.
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810197
Subject(s) - multiplicative function , combinatorics , mathematics , majorization , function (biology) , harmonic , mathematical physics , physics , mathematical analysis , quantum mechanics , evolutionary biology , biology
This paper investigates the Schur multiplicative and harmonic convexities of the complete symmetric function \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$F_n(x,r)=\sum _{i_1+i_2+\cdots +i_n=r}x_1^{i_1}x_2^{i_2}\ldots x_n^{i_n}$\end{document} and the function \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\varphi _n(x,r)=\frac{F_n(x,r)}{F_n(x,r-1)}$\end{document} , where i 1 , i 2 , …, i n are nonnegative integers and r ⩾ 1. As applications, some analytic inequalities are established by use of the theory of majorization. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim