Okeke, Godwin AmechiAbbas, Mujahid2015-08-032015-08-032015-04-28Okeke, 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. 1-11.1025-5834 (print)1029-242X (online)10.1186/s13660-015-0666-8http://hdl.handle.net/2263/49214The 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© 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.Ishikawa-type random iterative schemeMann-type random iterative schemeAlmost sure T-stabilitySeparable Banach spacesBochner integrabilityGeneralized φ-weakly contractive random operatorArticle