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The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications

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  • Chu, Yu-Ming
  • Xia, Wei-Feng
  • Zhang, Xiao-Hui

Abstract

For x=(x1,x2,…,xn)∈R+n, the second dual form of the Hamy symmetric function is defined by Hn∗∗(x,r)=Hn∗∗(x1,x2,…,xn;r)=∏1≤i1

Suggested Citation

  • Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:412-421
    DOI: 10.1016/j.jmva.2011.08.004
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    1. Ebrahimi, Nader & Spizzichino, Fabio, 1997. "Some results on normalized total time on test and spacings," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 231-243, December.
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    Cited by:

    1. Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    2. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    3. Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    4. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    5. Peide Liu & Xinli You, 2018. "Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-26, March.
    6. Wei-Feng Xia & Xiao-Hui Zhan & Gen-Di Wang & Yu-Ming Chu, 2012. "Some properties for a class of symmetric functions with applications," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(3), pages 227-249, June.

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