New results about quadratic functional equation on semigroups

Ahmed Akkaoui; Brahim Fadli

Published: 2024-11-19

Vol. 39 No. 2 (2025)

New results about quadratic functional equation on semigroups

Ahmed Akkaoui

, Brahim Fadli

Abstract

Let S be a semigroup, let (H, +) be a uniquely 2-divisible, abelian group and let ϕ, ψ be two endomorphisms of S that need not be involutive. In this paper, we express the solutions f : S→H of the following quadratic functional equation
f(xϕ(y)) + f(ψ(y)x) = 2f(x) + 2f(y), x,y ∈ S,
in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. Some applications of this result are presented.

Keywords:

quadratic functional equation , symmetrized additive Cauchy equation , additive function , bi-additive function , semigroup , endomorphism

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Akkaoui, A., & Fadli, B. (2024). New results about quadratic functional equation on semigroups. Annales Mathematicae Silesianae, 39(2), 209–222. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/18119

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Ahmed Akkaoui

ahmed.maths78@gmail.com
https://orcid.org/0000-0001-8468-3408

Affiliation:

Department of Mathematics, Faculty of Sciences, IBN TOFAIL University Morocco

Brahim Fadli

Affiliation:

Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University Morocco

Vol. 39 No. 2 (2025)
Published: 2025-09-01

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

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