Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 81045, 12 pages
On random coincidence and fixed points for a pair of multivalued and single-valued mappings
1Faculty of Mechanical Engineering, University of Belgrade, Aleksinačkih Rudara 12-35, Belgrade 11070, Serbia and Montenegro
2Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea
3Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Belgrade 11000, Serbia and Montenegro
Received 2 February 2006; Revised 21 June 2006; Accepted 22 July 2006
Copyright © 2006 Ljubomir B. Ćirić et al. 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.
Let () be a Polish space, the family of all nonempty
closed and bounded subsets of , and () a
measurable space. A pair of a hybrid measurable mappings and , satisfying the inequality (1.2), are introduced and
investigated. It is proved that if is complete, , are continuous for all , , are measurable for all , and for each , then there is a measurable
mapping such that for all . This result generalizes
and extends the fixed point theorem of Papageorgiou (1984) and many
classical fixed point theorems.