Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 4, Pages 341-349
doi:10.1155/S1048953301000302

Random fixed points for ∗-nonexpansive random operators

Abdul Rahim Khan1 and Nawab Hussain2

1King Fahd University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran 31261, Saudi Arabia
2Bahauddin Zakariya University, Centre for Advanced Studies in Pure and Applied Mathematics, Multan 60800, Pakistan

Received 1 December 1999; Revised 1 March 2001

Copyright © 2001 Abdul Rahim Khan and Nawab Hussain. 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

The notion of a ∗-nonexpansive multivalued map is different from that of a continuous map. In this paper we prove some fixed point theorems for ∗-nonexpansive multivalued random operators in the setup of Banach spaces and Fréchet spaces. Our work generalizes, refines and improves the earlier results of a number of authors.