THE STABILITY OF APPROXIMATELY ADDITIVE SOLUTIONS ON DAVISON EQUATIONS

Abstract

In this paper we study the Hyers-Ulam-Rassias stability theory by considering the case when the approximate remainder Á is defined by f(xy)+f(x+y)-f(xy+x)-f(y)=phi(x,y), where G is an algebra over the rational number field with a unit element e. E is a real or complex Hausdorff topological vector space, and f is a mapping from G into E. We prove theorems for the Hyers-Ulam-Rassias stability of Davison equations and obtain the corresponding error formulas.