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Proyecciones (Antofagasta)

Print version ISSN 0716-0917


ELQORACHI, Elhoucien  and  REDOUANI, Ahmed. Solutions and stability of a variant of Wilson's functional equation. Proyecciones (Antofagasta) [online]. 2018, vol.37, n.2, pp.317-344. ISSN 0716-0917.

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 (xy)+χ(y) 𝑓(σ(y)x)=2 𝑓(x) 𝑓(y), x,y ∈ G.

Keywords : Semigroup-Involution; D'Alembert's equation; Wilson's equation; Automorphism; Homomorphism; Multiplicative function; Hyers-Ulam stability; Superstability.

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