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Mathematica Slovaca

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Volume 68, Issue 2


A special class of functional equations

Ahmed Charifi / Radosław Łukasik / Driss Zeglami
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ms-2017-0110


We obtain in terms of additive and multi-additive functions the solutions f, h: SH of the functional equation


where (S, +) is an abelian monoid, Φ is a finite group of automorphisms of S, N = | Φ | designates the number of its elements, {aλ, λ ∈ Φ} are arbitrary elements of S and (H, +) is an abelian group. In addition, some applications are given. This equation provides a joint generalization of many functional equations such as Cauchy’s, Jensen’s, Łukasik’s, quadratic or Φ-quadratic equations.

Keywords: generalized polynomial function; Cauchy’s equation; Jensen’s equation; quadratic functional equation

MSC 2010: Primary 39B72, 39B52; Secondary 20B25, 47B39


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About the article

Received: 2015-10-05

Accepted: 2016-08-25

Published Online: 2018-03-31

Published in Print: 2018-04-25

Citation Information: Mathematica Slovaca, Volume 68, Issue 2, Pages 397–404, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0110.

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