# Solutions and stability of a variant of Wilson’s functional equation

• Elhoucien Elqorachi Ibn Zohr University.
• Ahmed Redouani Ibn Zohr University.

### Resumen

In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson’s functional equation (E) : f(xy) + χ(y)f(σ(y)x) = 2f(x)g(y), x, y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation f(xy) + χ(y)f(σ(y)x) = 2f(x)f(y), x, y ∈ G.

### Biografía del autor

Elhoucien Elqorachi, Ibn Zohr University.
Departamento de Matemáticas, Facultad de Ciencias.
Ahmed Redouani, Ibn Zohr University.
Departamento de Matemáticas, Facultad de Ciencias.

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