Prondanai Kaskasem - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok ۶۵۰۰۰, Thailand.
Aekarach Janchada - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok ۶۵۰۰۰, Thailand.
Chakkrid Klin-eam - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok ۶۵۰۰۰, Thailand and Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, ۶۵۰۰۰, Thailand.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[    fleft( sqrt[۳]{ax^۳ + by^۳}right)=af(x) + bf(y),]    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.

Hyers-Ulam-Rassias stability, radical cubic functional equation, quasi-$beta$-normed spaces, subadditive function