Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping

Abstract

Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces.