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

  • K. H. Sabour
  • A. Charifi
  • S. Kabbaj
Chapter

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
$$\displaystyle f(xy)+\mu (y)f(\varphi (y)x)=2f(x)f(y), $$
and μ-Wilson’s functional equation
$$\displaystyle f(xy)+\mu (y)f(\varphi (y)x)=2f(x)g(y), $$
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.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • K. H. Sabour
    • 1
  • A. Charifi
    • 1
  • S. Kabbaj
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesUniversity of Ibn TofailKenitraMorocco

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