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Schur convexity of Bonferroni means

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Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity of the Bonferroni means for n variables are investigated, and some mean value inequalities of n variables are established.

Abstract

Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity of the Bonferroni means for n variables are investigated, and some mean value inequalities of n variables are established.

참고문헌 (19)

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  5. B.-Y. Wang, "Foundations of majorization inequalities" (1990), Beijing Normal Univ. Press
  6. X.-M. Zhang, "Geometrically convex functions" (2004), Anhui University Press
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  8. Y.-M. Chu, "The Schur multiplicative and harmonic convexities of the complete symmetric function", Mathematische Nachrichten, 284(5-6), pp.653~663 (2011)
  9. J.-X. Meng, "The Schur-harmonic-convexity of dual form of the Hamy symmetric function", Matematicki Vesnik, 62, pp.37~46 (2010)
  10. K. Z. Guan, "SchurCconvexity for a class of symmetric function and its applica-tions", Math. Inequal. Appl., 9, pp.199~210 (2006)
  11. K. Z. Guan, "Some inequalities for a class of generalized means", J. Inequal. Pure Appl. Math., 5(3) (2004)
  12. N.-G. Zheng, "Schur-convexity of two types of one-parameter mean values in n variables", J. Inequal. Appl., 2007, pp.10~[DOI]
  13. W. F. Xia, "The Schur multiplicative convexity of the weighted generalized loga-rithmic mean in n variables", International Mathematical Forum, 4, pp.1229~1236 (2009)
  14. W.-F. Xia, "The Schur convexity of the weighted generalized logarithmic mean values according to harmonic mean", International Journal of Modern Mathematics, 4, pp.225~233 (2009)
  15. N.-G. Zheng, "The Schur- harmonic-convexity of two types of one-parameter mean values in n variables", Journal of Inequalities and Applications, 2007, pp.10~[DOI]
  16. Qian Xu, "Research on schur-p power-convexity of the quotient of arithmetic mean and geo-metric mean", Journal of Fudan University(Natural Science), 54, pp.299~295 (2015)
  17. N.-G. Zheng, "Convexity and Geometrical Convexity of the Identic and Logarithmic Means in N Variables", Acta Mathematica Scientia, 28A, pp.1173C~1180 (2008)
  18. D.S. Wang, "Schur-convexity for a mean of n variables with three parameters", Publications de l'Institut Mathmatique (Beograd)
  19. H.-N. Shi, "Majorization Theory and Analytic Inequality" (2012), Publishing House of Harbin Institute of Technology

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