On the superstability of the \(p\)-power-radical sine functional equation related to Pexider type
Volume 34, Issue 1, pp 52--64
https://dx.doi.org/10.22436/jmcs.034.01.05
Publication Date: February 14, 2024
Submission Date: December 15, 2023
Revision Date: December 23, 2023
Accteptance Date: January 03, 2024
Authors
W.-G. Park
- Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Korea.
M. Donganont
- School of Science, University of Phayao, Phayao 56000, Thailand.
G. H. Kim
- Department of Mathematics, Kangnam University, Yongin, Gyeonggi 16979, Korea.
Abstract
In this paper, we investigate the superstability bounded by a function (G{\v a}vruta sense) for the \(p\)-power-radical sine functional equation from
the \(p\)-power-radical Pexider type\rq{}s functional equation:
\[
f\left(\sqrt[p]{\frac{x+y}{2}}\right)^{2}-g\left(\sqrt[p]{\frac{x-y}{2}}\right)^{2}= h(\sqrt[p]{x})k(\sqrt[p]{y}),
\]
where \(p\) is an odd positive integer and \(f, g, h, k\) are complex valued functions on \(\mathbb{R}\).
Furthermore, the obtained results are extended to Banach algebras.
Share and Cite
ISRP Style
W.-G. Park, M. Donganont, G. H. Kim, On the superstability of the \(p\)-power-radical sine functional equation related to Pexider type, Journal of Mathematics and Computer Science, 34 (2024), no. 1, 52--64
AMA Style
Park W.-G., Donganont M., Kim G. H., On the superstability of the \(p\)-power-radical sine functional equation related to Pexider type. J Math Comput SCI-JM. (2024); 34(1):52--64
Chicago/Turabian Style
Park, W.-G., Donganont, M., Kim, G. H.. "On the superstability of the \(p\)-power-radical sine functional equation related to Pexider type." Journal of Mathematics and Computer Science, 34, no. 1 (2024): 52--64
Keywords
- Stability
- superstability
- sine functional equation
- \(p\)-radical functional equation
- \(p\)-power-radical functional equation
MSC
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