Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 23297, 19 pages
doi:10.1155/JAMSA/2006/23297
Equivalence and stability of random fixed point iterative
procedures
1Centre for Advanced Studies in Mathematics, School of Arts and Sciences,
Lahore University of Management Sciences (LUMS), Lahore 54792, Pakistan
2Department of Mathematics, Government Post
Graduate College, Sahiwal, Pakistan
Received 21 October 2004; Revised 18 February 2005; Accepted 2 March 2005
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 generate a sequence of measurable mappings iteratively and
study necessary conditions for its strong convergence to a random
fixed point of strongly pseudocontractive random operator. We
establish the weak convergence of an implicit random iterative
procedure to common random fixed point of a finite family of
nonexpansive random operators in Hilbert spaces. We prove the
equivalence between the convergence of random Ishikawa and random
Mann iterative schemes for contraction random operator and
strongly pseudocontractive random operator. We also examine the
stability of random fixed point iterative procedures for the
random operators satisfying certain contractive
conditions in the context of metric spaces.