Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-02010901202003012-Banach stability results for the radical cubic functional equation related to quadratic mapping3551671936ENR. E.GhaliDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, MoroccoS.KabbajDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, MoroccoJournal Article20190225The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation<br />$$<br />fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},<br />$$<br />for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces by using an analogue theorem of Brzdc{e}k in [17].http://jlta.iauctb.ac.ir/article_671936_a4036e8303fca99848e2005b99b3fe79.pdf