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Comment on "On the stability of quadratic double centralizers on Banach algebras" [M. Eshaghi Gordji, A. Bodaghi, J. Comput. Anal. Appl. 13 (2011), 724-729]
- Issue Date
- Nov-2012
- Publisher
- EUDOXUS PRESS, LLC
- Keywords
- Hyers-Ulam stability; Quadratic functional equation; Quadratic double centralizer
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v.14, no.7, pp.1299 - 1302
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Volume
- 14
- Number
- 7
- Start Page
- 1299
- End Page
- 1302
- ISSN
- 1521-1398
- Abstract
- Eshaghi Gordji and Bodaghi [2] proved the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f (kx + y) + f (kx - y) = 2k(2) f (x) + 2f (y) & f (xy) = f (x)y for a fixed integer k greater than 1. One can easily show that all the quadratic double centralizers (L, R) in the results are (0, 0). The results are trivial. In this paper, we correct the results. Using the direct method, we prove the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f (kx + y) + f (kx - y) = 2k(2) f (x) + 2f (y) & f (xy) = f (x)y(2) for a fixed integer k greater than 1.
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Related Researcher
- Park, Choonkil
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)