On a Variant of μ-Wilson’s Functional Equation with an Endomorphism

K. H. Sabour (), A. Charifi () and S. Kabbaj ()
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K. H. Sabour: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences
A. Charifi: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences
S. Kabbaj: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 93-111 from Springer

Abstract: Abstract The main goal of this chapter is to find the solutions (f, g) of the generalized variant of μ-d’Alembert’s functional equation f ( x y ) + μ ( y ) f ( φ ( y ) x ) = 2 f ( x ) f ( y ) , $$\displaystyle f(xy)+\mu (y)f(\varphi (y)x)=2f(x)f(y), $$ and μ-Wilson’s functional equation f ( x y ) + μ ( y ) f ( φ ( y ) x ) = 2 f ( x ) g ( y ) , $$\displaystyle f(xy)+\mu (y)f(\varphi (y)x)=2f(x)g(y), $$ in the setting of semigroups, monoids, and groups, where φ is an endomorphism not necessarily involutive and μ is a multiplicative function. We prove that their solutions can be expressed in terms of multiplicative and additive functions. Many consequences of these results are presented.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_5

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DOI: 10.1007/978-3-030-28950-8_5

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