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On the homogenization of means

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Abstract

The aim of this paper is to introduce several notions of homogenization in various classes of weighted means, which include quasiarithmetic and semideviation means. In general, the homogenization is an operator which attaches a homogeneous mean to a given one. Our results show that, under some regularity or convexity assumptions, the homogenization of quasiarithmetic means are power means, and homogenization of semideviation means are homogeneous semideviation means. In other results, we characterize the comparison inequality, the Jensen concavity, and Minkowski- and Hölder-type inequalities related to semideviation means.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Pf. 400, 4002, Debrecen, Hungary

    ZS. Páles

  2. Institute of Mathematics, Pedagogical University of Cracow, Podchorążych str. 2, 30-084, Cracow, Poland

    P. Pasteczka

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  1. ZS. Páles
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  2. P. Pasteczka
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Correspondence to ZS. Páles.

Additional information

The research of the first author was supported by the Hungarian Scientific Research Fund (OTKA) Grant K-111651 and by the EFOP-3.6.2-16-2017-00015 project. This project is cofinanced by the European Union and the European Social Fund.

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Páles, Z., Pasteczka, P. On the homogenization of means. Acta Math. Hungar. 159, 537–562 (2019). https://doi.org/10.1007/s10474-019-00944-3

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