2-Banach stability results for the radical cubic functional equation related to quadratic mapping

Subject Areas : Difference and functional equations

R. E.  Ghali ¹ (Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco)
S.  Kabbaj ² (Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco)

Received: 2019-02-25 Accepted : 2019-12-28 Published : 2020-03-01

Keywords: Stability, hyperstability, 2-Banach spaces, radical functional equation,

Abstract :

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadraticfunctional equation$$f\left(\sqrt[3]{ax^{3}+by^{3}}\right)+f\left(\sqrt[3]{ax^{3}-by^{3}}\right)=2a^{2}f(x)+2b^{2}f(y),\;\; x,y\in\mathbb{R},$$for a mapping $f$ from $\mathbb{R}$ into a vector space.We also investigate some stability and hyperstability results forthe considered equation in 2-Banach spaces by using an analogue theorem of Brzd\c{e}k in [17].

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