A parametric functional equation originating from number theory

Aziz Mouzoun; Driss Zeglami; Youssef Aissi

Published: 2022-01-17

Vol. 36 No. 1 (2022)

A parametric functional equation originating from number theory

Aziz Mouzoun

, Driss Zeglami , Youssef Aissi

Abstract

Let S be a semigroup and α,β∈ℝ. The purpose of this paper is to determine the general solution f:ℝ²→S of the following parametric functional equation
f(x₁x₂+αy₁y₂,x₁y₂+x₂y₁+βy₁y₂) = f(x₁,y₁)f(x₂,y₂),
for all (x₁,y₁), (x₂,y₂)∈ℝ², that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices.

Keywords:

functional equation , number theory , character , multiplicative function , monoid , additive function

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Mouzoun, A., Zeglami, D., & Aissi, Y. (2022). A parametric functional equation originating from number theory. Annales Mathematicae Silesianae, 36(1), 71–91. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13462

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Aziz Mouzoun

mouzounposte@gmail.com
https://orcid.org/0000-0001-7966-0391

Affiliation:

Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco Morocco

Driss Zeglami

Affiliation:

Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco Morocco

Youssef Aissi

Affiliation:

Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco Morocco

Vol. 36 No. 1 (2022)
Published: 2022-03-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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