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Aequationes mathematicae

, Volume 90, Issue 1, pp 211–233 | Cite as

From a theorem of R. Ger and T. Kochanek to marginal joints of means

  • Zoltán DaróczyEmail author
  • Justyna Jarczyk
  • Witold Jarczyk
Open Access
Article

Abstract

We answer in the negative a problem posed in Daróczy (Report on 52nd International Symposium on Functional Equations. Aequat. Math., 2015) by the first author, in connection with a result of Ger and Kochanek (Colloq Math 115:87–99, 2009), and its generalization formulated in Daróczy et al. (Report on 52nd International Symposium on Functional Equations. Aequat. Math., 2015). A further generalization is posed as an open problem. Elaborating an idea of the construction of means presented in Examples 1.2 and 1.4 we come to the notion of marginal joints of means. It provides a pretty wide class of means extending two given means on adjacent intervals.

Keywords

Mean Quasi-arithmetic mean Generalized Jensen’s equation Extension of means Marginal joint of means 

Mathematics Subject Classification

Primary 26E60 Secondary 39B22 

References

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Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Zoltán Daróczy
    • 1
    Email author
  • Justyna Jarczyk
    • 2
  • Witold Jarczyk
    • 2
  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary
  2. 2.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielonaPoland

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