On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces

Abstract

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation<br />[<br /> fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),<br />]<br /> where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generalized radical cubic functional equations in $(beta,p)$-Banach spaces.