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

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Authors

Okeke, Godwin Amechi
Abbas, Mujahid

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SpringerOpen

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).

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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

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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.