Published: 2024-11-19
Language: EN

New results about quadratic functional equation on semigroups

Ahmed Akkaoui Logo ORCID , 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((y)) + f(ψ(y)x) = 2f(x) + 2f(y),   x,yS,
in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. Some applications of this result are presented.

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Citation rules

Akkaoui, A., & Fadli, B. (2024). New results about quadratic functional equation on semigroups. Annales Mathematicae Silesianae. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/18119

2024
Published: 2023-10-26


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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