Wilson’s functional equation with an endomorphism

Khalid Sabour

Résumé


In the present paper, we determine the complex-valued solutions ( f ;g) of the functional equation f (xy)+ f (j(y)x) = 2 f (x)g(y);
in the setting of groups and monoids, where j is an endomorphism not necessarity involutive. We prove that their solutions can be expressed in terms of multiplicative and additive functions. Many consequences of these results are presented.

Mots-clés


Functional equation, Wilson, endomorphism, monoid, multiplicative function.

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