Stability and common stability for the systems of linear equations and its applications

Abstract

In this paper some results about the Hyers-Ulam-Rassias stability for the linear functional equations in general form and its Pexiderized can be proved for given functions on general domain to a complex Banach spaces under some suitable conditions. In connection with the problem of G. L. Forti in the 13st ICFEI we consider the common stability for the systems of functional equations and our aim is to establish some common Hyers-Ulam-Rassias stability for systems of homogeneous linear functional equations. The results is applied to the study of some superstability results for the exponential functional equation.