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.2011.26.1.23
Published 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
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