Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 23297, 19 pages

Equivalence and stability of random fixed point iterative procedures

Ismat Beg1 and Mujahid Abbas1

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.


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.