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On random coincidence and fixed points for a pair of multivalued and single-valued mappings

  • Ljubomir B. Ćirić1Email author,
  • Jeong S. Ume2 and
  • Siniša N. Ješić3
Journal of Inequalities and Applications20062006:81045

https://doi.org/10.1155/JIA/2006/81045

©  Ljubomir B. Ćirić et al. 2006

Received: 2 February 2006

Accepted: 22 July 2006

Published: 18 October 2006

Abstract

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.

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Authors’ Affiliations

(1)
Faculty of Mechanical Engineering, University of Belgrade
(2)
Department of Applied Mathematics, Changwon National University
(3)
Faculty of Electrical Engineering, University of Belgrade

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Copyright

© Ljubomir B. Ćirić et al. 2006

This article is published under license to BioMed Central Ltd. 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.