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 Composite implicit random iterations for approximating common random fixed point for a finite family of asymptotically nonexpansive random operators Commun. Korean Math. Soc. 2011 Vol. 26, No. 1, 23-35 https://doi.org/10.4134/CKMS.2011.26.1.23Published online March 1, 2011 Shrabani Banerjee and Binayak S. Choudhury Bengal Engineering and Science University, Bengal Engineering and Science University Abstract : In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces. Keywords : composite implicit random iterative process with errors, asymptotically nonexpansive random operators, Condition$(B)$, Banach spaces, measurable spaces MSC numbers : 47H10 Downloads: Full-text PDF