Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 89213, 16 pages
doi:10.1155/JAMSA/2006/89213
Convergence of iterative algorithms to common random fixed points of random operators
Department of Mathematics, Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, Lahore 54792, Pakistan
Received 17 January 2006; Revised 27 June 2006; Accepted 6 July 2006
This work is dedicated to Professor S. P. Singh on his 70th birthday
Copyright © 2006 Ismat Beg and Mujahid Abbas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove the existence of a common random
fixed point of two asymptotically nonexpansive random operators through
strong and weak convergences of an iterative process. The necessary and
sufficient condition for the convergence of sequence of measurable functions
to a random fixed point of asymptotically quasi-nonexpansive random
operators in uniformly convex Banach spaces is also established.