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

• Elqorachi, Elhoucien ^[1] ; Redouani, Ahmed ^[1]
  1. [1] Université Ibn Zohr

     Université Ibn Zohr

     Agadir, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 2, 2018, págs. 317-344
• Idioma: inglés
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• 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.