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Acta Mathematica Hungarica

, Volume 132, Issue 1–2, pp 92–106 | Cite as

Invariance of the Cauchy means with respect to Lagrange mean-type mappings of the same generators

  • Janusz MatkowskiEmail author
Article

Abstract

Without any regularity conditions, we determine all the Cauchy means C [f,g] that are invariant with respect to the mean-type mapping (L [f],L [g]) where L [f] denotes the Lagrangean mean generated by f. Applications in iteration theory and functional equation are given.

Key words and phrases

invariant mean Cauchy mean Lagrangean mean differential equation functional equation 

2000 Mathematics Subject Classification

26E60 34A05 39B22 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Science and EconometryUniversity of Zielona GóraZielona GóraPoland
  2. 2.Institute of MathematicsSilesian UniversityKatowicePoland

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