Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator

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dc.contributor.author Okeke, Godwin Amechi
dc.contributor.author Abbas, Mujahid
dc.date.accessioned 2015-08-03T05:11:31Z
dc.date.available 2015-08-03T05:11:31Z
dc.date.issued 2015-04-28
dc.description.abstract The aim of this paper is to introduce the concept of generalized φ-weakly contraction random operators and then to prove the convergence and almost sure T-stability of Mann and Ishikawa-type random iterative schemes. We also prove that a random fixed point of such operators is Bochner integrable. Our results generalize, extend and improve various results in the existing literature including the results in Berinde (Bul. ¸Stiin¸t. - Univ. Baia Mare, Ser. B Fasc. Mat.-Inform. 18(1):7-14, 2002), Olatinwo (J. Adv. Math. Stud. 1(1):5-14, 2008), Rhoades (Trans. Am. Math. Soc. 196:161-176, 1974; Indian J. Pure Appl. Math. 21(1):1-9, 1990; Indian J. Pure Appl. Math. 24(11):691-703, 1993) and Zhang et al. (Appl. Math. Mech. 32(6):805-810, 2011). en_ZA
dc.description.librarian am2015 en_ZA
dc.description.sponsorship The first author is grateful to the Covenant University Centre for Research and Development (CUCERD) for supporting his research. en_ZA
dc.description.uri http://www.journalofinequalitiesandapplications.com en_ZA
dc.identifier.citation Okeke, GA & Abbas, M 2015, 'Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator', Journal of Inequelities and Applications, vol. 2015, art. 146, pp. 1-11. en_ZA
dc.identifier.issn 1025-5834 (print)
dc.identifier.issn 1029-242X (online)
dc.identifier.other 10.1186/s13660-015-0666-8
dc.identifier.uri http://hdl.handle.net/2263/49214
dc.language.iso en en_ZA
dc.publisher SpringerOpen en_ZA
dc.rights © 2015 Okeke and Abbas; licensee Springer. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. en_ZA
dc.subject Ishikawa-type random iterative scheme en_ZA
dc.subject Mann-type random iterative scheme en_ZA
dc.subject Almost sure T-stability en_ZA
dc.subject Separable Banach spaces en_ZA
dc.subject Bochner integrability en_ZA
dc.subject Generalized φ-weakly contractive random operator en_ZA
dc.title Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator en_ZA
dc.type Article en_ZA


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