Wilson’s functional equation with an endomorphism

Khalid Sabour


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.


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

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