International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 23486, 15 pages
doi:10.1155/IJMMS/2006/23486
Common random fixed points of compatible random operators
Department of Mathematics and Center for Advanced Studies in Mathematics, Lahore University of Management Sciences, Lahore 54792, Pakistan
Received 2 June 2005; Revised 12 April 2006; Accepted 25 April 2006
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 construct a random iteration scheme and study necessary conditions for its convergence to a common random fixed point of two pairs of compatible random operators satisfying Meir-Keeler type conditions in Polish spaces. Some random fixed point theorems for weakly compatible random operators under generalized contractive conditions in the framework of symmetric spaces are also proved.