Representation and perturbations of a system of additive-quadratic functional equations

In the present article, we introduce a novel multimixed additive-quadratic mapping, and then show that the system of several mixed additive-quadratic equations defining a multimixed additive-quadratic mapping can be described as one single equation. We also show that such mappings under some conditions are multi-additive, multi-quadratic and multi-additive-quadratic. Moreover, we prove the Hyers stability for the multi-additive, multi-quadratic and multi-additive-quadratic mappings in the content of Banach spaces by two famous classical manners. As a outcome, by using a decomposition, we show that every multimixed additive-quadratic mapping is Hyers stable.

کلیدواژه ها:

Banach space ، Hyers-Ulam stability ، Multi-additive mapping ، multi-quadratic mapping ، Multi-additive-quadratic mapping