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

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Frontiers in Functional Equations and Analytic Inequalities

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(xσ(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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Author information

Authors and Affiliations

  1. Laboratory LIMATI, Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Belaid Bouikhalene

  2. Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco

    Elhoucien Elqorachi

Authors
  1. Belaid Bouikhalene
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  2. Elhoucien Elqorachi
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Corresponding author

Correspondence to Belaid Bouikhalene .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Bouikhalene, B., Elqorachi, E. (2019). A Class of Functional Equations of Type d’Alembert on Monoids. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_13

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