SUMA Publishing Group
Results in Fixed Point Theory and Applications
2581-6047
2019
2019
August
02
Comments on some Fixed Point Theorems
1
14
EN
Laddawan Aiemsomboon
Aiemsomboon
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121,
Thailand.
wutiphol@mathstat.sci.tu.ac.th
Wutiphol
t
Sintunavara
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121,
Thailand.
wutiphol@mathstat.sci.tu.ac.th
https://doi.org/10.30697/rfpta-2019-012
The goal of this paper is to investigate the general solution and the hyperstability results of the generalized $p$-radical functional equation
\begin{equation*}
f\left(\sqrt[p]{\sum_{i=1}^kx_i^p}\right)=\sum_{i=1}^kf(x_i)
\end{equation*}
for all $x_1,\dots,x_k \in \mathbb{R}$,
where $f: \mathbb{R} \to Y$ is a mapping, $p$ is a natural number, $k$ is a natural number such that $k \geq 2$, and $Y$ is a quasi-Banach space. Furthermore, the hyperstablity result for the inhomogeneous generalized $p$-radical functional equations is derived from the main results. Finally, we give the illustrative example showing the validity of the obtained results while the main results of Almahalebi et al. is not applicable.
Fixed point; hyperstability; quasi-Banach space; $p$-radical functional equation.
https://www.researchinthefixedpointtheory.com/2019/08/02/new-hyperstability-results-generalized-p-radical-functional-equation-quasi-banach-spaces-illustrative-example/
https://www.researchinthefixedpointtheory.com/wp-content/uploads/2019/08/RFPTA-2019-012.pdf