The stability of bi-derivations and bihomomorphisms in Banach algebras
Authors
S. Khan
- Department of Mathematics, , , Korea, Hanyang University, Seoul 04763, Korea.
Ch. Park
- Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea.
M. Donganont
- School of Science, University of Phayao, Phayao 56000, Thailand.
Abstract
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of bi-derivations and bihomomorphisms in Banach algebras,
associated with the bi-additive functional inequality
\[
\| f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) + f(x-y, z-w) -4f(x,z)\| \\ \quad \le \left \|s \left(2f\left(x+y, z-w\right) + 2f\left(x-y, z+w\right) - 4f(x,z )+ 4 f(y, w)\right)\right\| ,
\]
where \(s\) is a fixed nonzero complex number with \(|s |< 1\).
Share and Cite
ISRP Style
S. Khan, Ch. Park, M. Donganont, The stability of bi-derivations and bihomomorphisms in Banach algebras, Journal of Mathematics and Computer Science, 35 (2024), no. 4, 482--491
AMA Style
Khan S., Park Ch., Donganont M., The stability of bi-derivations and bihomomorphisms in Banach algebras. J Math Comput SCI-JM. (2024); 35(4):482--491
Chicago/Turabian Style
Khan, S., Park, Ch., Donganont, M.. "The stability of bi-derivations and bihomomorphisms in Banach algebras." Journal of Mathematics and Computer Science, 35, no. 4 (2024): 482--491
Keywords
- Hyers-Ulam stability
- biderivation on Banach algebra
- bihomomorphism in Banach algebra
- fixed point method
- bi-additive functional inequality
MSC
- 39B52
- 47H10
- 39B72
- 47B47
- 17B40
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