Characterization and stability of multi-additive-quadratic-cubic mappings

Abstract

In this work, we introduce a system of additive, quadratic and cubic functional equations (somewhat different from what has been defined by Bodaghi and Rassias) which defines the multi-additive-quadratic-cubic mappings and then unify and characterize such mappings as a single equation without the quadratic condition. Moreover, by using a fixed point theorem, we establish the Găvruţa stability of the multi-additive-quadratic-cubic mappings in the setting of Banach spaces. As few known results, we prove the Hyers stability for multi-additive, multi-quadratic and multi-cubic mappings.