Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2017: 0.314
5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339
Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 2

Issues

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

Abstract

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

λΦf(x+λy+aλ)=Nf(x)+h(y),x,yS,

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

References

  • [1]

    Baker, J. A.: A general functional equation and its stability, Proc. Amer. Math. Soc. 133 (2005), 1657–1664.CrossrefGoogle Scholar

  • [2]

    Charifi, A.—Almahalebi, M.—Kabbaj, S.: A generalization of Drygas functional equation, Proyecciones 35 (2016), 159–176.CrossrefGoogle Scholar

  • [3]

    Charifi, A.—Zeglami, D.—Kabbaj, S.: Solution of generalized Jensen and quadratic functional equations, submited.Google Scholar

  • [4]

    Chung, J. K.—Ebanks, B. R.—Ng, C. T.—Sahoo, P. K.: On a quadratic trigonometric functional equation and some applications, Trans. Amer. Math. Soc. 347 (1995), 1131–1161.CrossrefGoogle Scholar

  • [5]

    Czerwik, S.: On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59–64.CrossrefGoogle Scholar

  • [6]

    Ebanks, B. R.—Kannappan, PL.—Sahoo, P. K.: A common generalization of functional equations characterizing normed and quasi-inner-product spaces, Canad. Math. Bull. 35 (1992), 321–327.CrossrefGoogle Scholar

  • [7]

    Fadli, B.—Zeglami, D.—Kabbaj, S.: On a Gajda’s type quadratic equation on a locally compact abelian group, Indagationes Math. 26 (2015), 660–668.CrossrefGoogle Scholar

  • [8]

    Fadli, B.—Zeglami, D.—Kabbaj, S.: A variant of Jensen’s functional equation on semigroups, Demonstratio Math. 49 (2016), 413–420.Google Scholar

  • [9]

    Łukasik, R.: Some generalization of Cauchy’s and the quadratic functional equations, Aequationes Math. 83 (2012), 75–86.CrossrefGoogle Scholar

  • [10]

    Stetkæ r, H.: Functional equations on abelian groups with involution, Aequationes Math. 54 (1997), 144–172.CrossrefGoogle Scholar

  • [11]

    Stetkæ r, H.: Functional equations involving means of functions on the complex plane, Aequationes Math. 55 (1998), 47–62.Google Scholar

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.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in