Okeke, G.A. and Abbas, Mujahid (2015) Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator. Journal of Inequalities and Applications.
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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
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Ishikawa-type random iterative scheme; Mann-type random iterative scheme; almost sure T-stability; separable Banach spaces; Bochner integrability; generalized φ-weakly contractive random operator |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | Mrs Patricia Nwokealisi |
| Date Deposited: | 25 Sep 2015 15:16 |
| Last Modified: | 25 Sep 2015 15:16 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/5494 |
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