TY - JOUR ID - 37191 TI - On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$\beta$-Banach Spaces JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Kaskasem, Prondanai AU - Janchada, Aekarach AU - Klin-eam, Chakkrid AD - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. AD - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand and Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand. Y1 - 2020 PY - 2020 VL - 17 IS - 1 SP - 69 EP - 90 KW - Hyers-Ulam-Rassias stability KW - radical cubic functional equation KW - quasi-$beta$-normed spaces KW - subadditive function DO - 10.22130/scma.2018.87694.451 N2 - 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. UR - https://scma.maragheh.ac.ir/article_37191.html L1 - https://scma.maragheh.ac.ir/article_37191_17fbaf21d3cb91211779fc3cc33971f0.pdf ER -