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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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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