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A Class of Functional Equations of Type d’Alembert on Monoids

  • Belaid BouikhaleneEmail author
  • Elhoucien Elqorachi
Chapter

Abstract

Recently, the solutions of the functional equation f(xy) − f(σ(y)x) = g(x)h(y) obtained, where σ is an involutive automorphism and f, g, h are complex-valued functions, in the setting of a group G and a monoid S. Our main goal is to determine the general complex-valued solutions of the following version of this equation, viz. f(xy) − μ(y)f(σ(y)x) = g(x)h(y) where \(\mu : G\longrightarrow \mathbb {C}\) is a multiplicative function such that μ((x)) = 1 for all x ∈ G. As an application we find the complex-valued solutions (f, g, h) on groups of equation f(xy) + μ(y)g(σ(y)x) = h(x)h(y) on monoids.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratory LIMATI, Polydisciplinary FacultySultan Moulay Slimane UniversityBeni MellalMorocco
  2. 2.Department of Mathematics, Faculty of SciencesIbn Zohr UniversityAgadirMorocco

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