Fixed points and quadratic equations connected with homomorphisms and derivations on non-Archimedean algebras

Abstract

We apply the fixed point method to prove the stability of the systems of functional equations {f(xy) = f(x)f(y); f(ax + by) + f(ax - by) = 2a(2)f(x) + 2b(2)f(y), {f(xy) = x(2)f(y) + f(x)y(2); f(ax + by) + f(ax - by) = 2a(2)f(x) + 2b(2)f(y), on non-Archimedean Banach algebras. Moreover, we give some applications of our results in non-Archimedean Banach algebras over p-adic numbers.