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Results in Mathematics

, Volume 71, Issue 1–2, pp 397–410 | Cite as

Explicit Solutions of the Invariance Equation for Means

  • Janusz Matkowski
  • Monika Nowicka
  • Alfred WitkowskiEmail author
Open Access
Article

Abstract

Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in Kahlig and Matkowski (Math Inequal Appl 18(3):1143–1150, 2015), and then, more generally, given a bivariate symmetric, homogeneous and monotone mean M, we give explicit formula for a rich family of pairs of M-complementary means. We prove that this method cannot be extended for higher dimension. Some examples are given and two open questions are proposed.

Keywords

Invariant means homogeneous means 

Mathematics Subject Classification

26D15 

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Copyright information

© The Author(s) 2016

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

  • Janusz Matkowski
    • 1
  • Monika Nowicka
    • 2
  • Alfred Witkowski
    • 2
    Email author
  1. 1.Faculty of Mathematics, Computer Sciences and EconometricsUniversity of Zielona GoraZielona GóraPoland
  2. 2.Institute of Mathematics and PhysicsUTP University of Science and TechnologyBydgoszczPoland

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