On the alienation of multiplicative and additive functions

Mohamed Chakiri; Abdellatif Chahbi; Elhoucien Elqorachi

Published: 2024-11-15

2024

On the alienation of multiplicative and additive functions

Mohamed Chakiri

, Abdellatif Chahbi , Elhoucien Elqorachi

Abstract

Given S a semigroup. We study two Pexider-type functional equations
f(xy) + g(xy) = f(x) + f(y) + g(x)g(y), x,y ∈ S,
and
∫_Sf(xyt)dμ(t) + ∫_Sg(xyt)dμ(t) = f(x) + f(y) + g(x)g(y), x,y ∈ S,
for unknown functions f and g mapping S into ℂ, where μ is a linear combination of Dirac measures (δ_z_{_i}})_i∈I for some fixed elements (z_i)_i∈I contained in S such that ∫_Sdμ(t) = 1.
The main goal of this paper is to solve the above two functional equations and examine whether or not they are equivalent to the systems of equations
f(xy) = f(x) + f(y), g(xy) = g(x)g(y), x,y ∈ S,
and
∫_Sf(xyt)dμ(t) = f(x) + f(y), ∫_Sg(xyt)dμ(t) = g(x)g(y), x,y ∈ S,
respectively.

Keywords:

alienation , semigroup , multiplicative function , additive function , quadratic equivalence

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Chakiri, M., Chahbi, A., & Elqorachi, E. (2024). On the alienation of multiplicative and additive functions. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/18110

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Mohamed Chakiri

medchakiri@hotmail.com
https://orcid.org/0009-0002-0297-9390

Affiliation:

Department of Mathematics, Faculty of Sciences, Ibn Zohr University Morocco

Abdellatif Chahbi

Affiliation:

Department of Mathematics, Faculty of Sciences, Ibn Zohr University Morocco

Elhoucien Elqorachi

Affiliation:

Department of Mathematics, Faculty of Sciences, Ibn Zohr University Morocco

2024
Published: 2024-01-18

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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