On the stability of a radical cubic functional equation in quasi- $${\beta}$$ β -spaces

Abstract

In this paper, we introduce and solve the radical cubic functional equation $$f\left({\sqrt[3]{x^{3} + y^{3}}}\right)= f(x) + f(y).$$ We also establish stability in quasi-\({\beta}\)-Banach spaces, and then the stability by using subadditive and subquadratic functions for the radical cubic functional equation in (\({\beta}\), p)-Banach spaces is given.