On the Stability of Generalized Additive Functional Inequalities in Banach Spaces

Abstract

We study the following generalized additive functional inequality ‖af(x)+bf(y)+cf(z)‖≤‖f(αx+βy+γz)‖, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.