Approximate Multipliers And Approximate Double Centralizers: A fixed Point Approach

Abasalt Bodaghi; Madjid Eshaghi Gordji; Kamal Paykan

doi:10.2478/v10309-012-0052-1

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Approximate Multipliers And Approximate Double Centralizers: A fixed Point Approach

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 3 (December 2012)

By: Abasalt Bodaghi, Madjid Eshaghi Gordji and Kamal Paykan

Open Access

|May 2013

Abstract

In the present paper, the Hyers-Ulam stability and also the super-stability of double centralizers and multipliers on Banach algebras are established by using a fixed point method. With this method, the condition of without order on Banach algebras is no longer necessary.

References

[1] A. Bodaghi, I. A. Alias and M. H. Ghahramani, Ulam stability of a quarticfunctional equation, Abst. Appl. Anal. Volume 2012, Art. ID 232630, 9 pages, doi:10.1155/2012/232630.10.1155/2012/232630
Search in Google Scholar
[2] A. Bodaghi, I. A. Alias and M. H. Ghahramani, Approximately cubicfunctional equations and cubic multipliers, J. Inequal. Appl. 2011 (2011): 53.10.1186/1029-242X-2011-53
Search in Google Scholar
[3] L. C˘adariu and V. Radu, Fixed points and the stability of quadraticfunctional equations, An. Univ. Timi，soara, Ser. Mat. Inform. 41 (2003), 25-48.
Search in Google Scholar
[4] L. C˘adariu and V. Radu, On the stability of the Cauchy functional equa-tion: A fixed point approach, Grazer Math. Ber. 346 (2004), 43-52.
Search in Google Scholar
[5] J. B. Diaz and B. Margolis, A fixed point theorem of the alternative forcontractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968),305-309.10.1090/S0002-9904-1968-11933-0
Search in Google Scholar
[6] M. Eshaghi Gordji and A. Bodaghi, On the Hyers-Ulam-Rasias stabilityproblem for quadratic functional equations, East. J. Approximations. 16, No. 2 (2010), 123-130.
Search in Google Scholar
[7] M. Eshaghi Gordji and A. Bodaghi, On the stability of quadratic doublecentralizers on Banach algebras, J. Comput. Anal. Appl. 13, No. 4 (2011), 724-729.
Search in Google Scholar
[8] M. Eshaghi Gordji, A. Bodaghi and C. Park, A fixed point approach to thestability of double Jordan centralizers and Jordan multipliers on Banachalgebras, U.P.B. Sci. Bull., Series A, 73, Iss. 2 (2011), 65-73.
Search in Google Scholar
[9] M. Eshaghi Gordji, H. Khodaei, The fixed point method for fuzzy approxi-mation of a functional equation associated with inner product spaces, Discrete Dynamics in Nature and Society Volume 2010, Article ID 140767, 15 pages, doi:10.1155/2010/140767.10.1155/2010/140767
Search in Google Scholar
[10] M. Eshaghi Gordji, M. B. Savadkouhi, Approximation of generalized ho-momorphisms in quasi-Banach algebras, Analele Univ. Ovidius Constata, Math series, Vol. 17(2), 2009, 203-214.
Search in Google Scholar
[11] S. Helgason, Multipliers of Banach algebras, Ann. Math. (2) 64 (1956), 240-254.10.2307/1969971
Search in Google Scholar
[12] G. Hochschild, Cohomology and representations of associative algebras, Duke Math. J. 14 (1947), 921-948.10.1215/S0012-7094-47-01473-7
Search in Google Scholar
[13] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.10.1073/pnas.27.4.222107831016578012
Search in Google Scholar
[14] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equationsin Several Variables, Birkh¨auser, Basel, 1998.10.1007/978-1-4612-1790-9
Search in Google Scholar
[15] B. E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc. 14 (1964), 299-320.10.1112/plms/s3-14.2.299
Search in Google Scholar
[16] T. Miura, G. Hirasawa and S. E. Takahashi, Stability of multipliers onBanach algebras, Internat. J. Math. Math. Sci. 45 (2004), 2377-2381.10.1155/S0161171204402324
Search in Google Scholar
[17] M. S. Moslehian, F. Rahbarnia, P. K. Sahoo, Approximate double center-alizers are exact double centeralizers, Bol. Soc. Mat. Mexicana. (3) Vol. 13 (2007).
Search in Google Scholar
[18] C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensenfunctional equations in Banach algebras, Fixed Point Theory and Applications. 2007 Art. ID 50175 (2007).10.1155/2007/50175
Search in Google Scholar
[19] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.10.1090/S0002-9939-1978-0507327-1
Search in Google Scholar
[20] M. Turinici, Sequentially iterative processes and applications to Volterrafunctional equations, Annales Univ. Mariae-Curie Sklodowska (Sect A). 32 (1978), 127-134.
Search in Google Scholar
[21] S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York, 1940.
Search in Google Scholar
[22] J. K. Wang, Multipliers of commutative Banach algebras, Pacific J. Math. 11 (1961), 1131-1149.10.2140/pjm.1961.11.1131
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10309-012-0052-1 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 21 - 32

Published on: May 21, 2013

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Banach algebra,

Double centralizer,

Hyers-Ulam stability,

Related subjects:

© 2013 Abasalt Bodaghi, Madjid Eshaghi Gordji, Kamal Paykan, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.

Volume 20 (2012): Issue 3 (December 2012)