Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

2 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand and Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand.

Abstract

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation
\[
    f\left( \sqrt[3]{ax^3 + by^3}\right)=af(x) + bf(y),
\]
    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.

Keywords

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