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

Journal of Linear and Topological Algebra

مقاله 3، دوره 09، شماره 01، خرداد 2020، صفحه 35-51   

نوع مقاله: Research Paper

نویسندگان

R. E. Ghali^* ؛ S. Kabbaj

Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco

چکیده

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional 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 for the considered equation in 2-Banach spaces by using an analogue theorem of Brzd\c{e}k in [17].

کلیدواژه‌ها

Stability؛ hyperstability؛ 2-Banach spaces؛ radical functional equation

مراجع

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