A Parametric Functional Equation Originating from Number Theory

Aziz Mouzoun; Driss Zeglami; Youssef Aissi

doi:10.2478/amsil-2022-0001

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A Parametric Functional Equation Originating from Number Theory

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 1 (March 2022)

By: Aziz Mouzoun , Driss Zeglami and Youssef Aissi

Open Access

|Jan 2022

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 $f (x_{1} + x_{2} + α y_{1} y_{2}, x_{1} y_{2} + x_{2} y_{1} + β y_{1} y_{2}) = f (x_{1}, y_{1}) f (x_{2}, y_{2}),$ f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1}{y_2} + {x_2}{y_1} + \beta {y_1}{y_2}} \right) = f\left( {{x_1},{y_1}} \right)f\left( {{x_2},{y_2}} \right), 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.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0001 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 71 - 91

Submitted on: Jan 10, 2021

Accepted on: Jan 3, 2022

Published on: Jan 17, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

functional equation,

number theory,

character,

multiplicative function,

monoid,

additive function

Related subjects:

Mathematics,

General mathematics

© 2022 Aziz Mouzoun, Driss Zeglami, Youssef Aissi, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 36 (2022): Issue 1 (March 2022)