Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Abstract

Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai)=D(a1)a22⋯an2+a12D(a2)a32⋯an2+⋯+a12a22⋯an−12D(an) for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.