2015/05/14 by Elqorachi Elhoucien, Elhoucien, Elqorachi, Redouani Ahmed +1
Mathematics · #39B32 #39B52 #39B82 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:39B32 #msc:39B52 #msc:39B82
paper · pdf · doi:10.48550/arxiv.1505.06512
19pages
arxiv created 2015/05/14 · arxiv updated 2015/05/26
In this paper we will investigate the 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.