Reducible means and reducible inequalities View Full Text


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Article Info

DATE

2017-01-06

AUTHORS

Tibor Kiss, Zsolt Páles

ABSTRACT

It is well-known that if a real valued function acting on a convex set satisfies the n-variable Jensen inequality, for some natural number n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 2$$\end{document}, then, for all k∈{1,⋯,n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\in \{1,\dots , n\}$$\end{document}, it fulfills the k-variable Jensen inequality as well. In other words, the arithmetic mean and the Jensen inequality (as a convexity property) are both reducible. Motivated by this phenomenon, we investigate this property concerning more general means and convexity notions. We introduce a wide class of means which generalize the well-known means for arbitrary linear spaces and enjoy a so-called reducibility property. Finally, we give a sufficient condition for the reducibility of the (M, N)-convexity property of functions and also for Hölder–Minkowski type inequalities. More... »

PAGES

505-525

References to SciGraph publications

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  • 2013. Functional Analysis, Calculus of Variations and Optimal Control in NONE
  • 1906-12. Sur les fonctions convexes et les inégalités entre les valeurs moyennes in ACTA MATHEMATICA
  • 1988. Nonlinear Functional Analysis and its Applications, IV: Applications to Mathematical Physics in NONE
  • 2009. An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality in NONE
  • 2010-04-21. Generalized weighted quasi-arithmetic means in AEQUATIONES MATHEMATICAE
  • 2003. Handbook of Means and Their Inequalities in NONE
  • 1971-02. A general inequality for means in AEQUATIONES MATHEMATICAE
  • 2015. Characterization of generalized quasi-arithmetic means in ACTA SCIENTIARUM MATHEMATICARUM
  • 1983. Inequalities for Homogeneous Means Depending on Two Parameters in GENERAL INEQUALITIES 3
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  • 1988. Means and Their Inequalities in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00010-016-0459-2

    DOI

    http://dx.doi.org/10.1007/s00010-016-0459-2

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    https://app.dimensions.ai/details/publication/pub.1027546962


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