The Pexiderized Cauchy functional equation on restricted domains and its asymptotic properties

Abstract

The aim of this paper is to investigate the stability of the Pexiderized
Cauchy functional equation
                                 f(x + y) = g(x) + h(y)
within certain restricted domains in normed spaces. The asymptotic behaviors and hyperstability results of this functional equation are also considered as an application. Our main results generalize and extend the main results obtained in [15, Theorem 3 and Corollary 4] and [18, Theorem 3.1 and Corollary 3.2].