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

Journal of Inequalities and Applications volume 2006, Article number: 81045 (2006) Cite this article

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 and Affiliations

  1. Faculty of Mechanical Engineering, University of Belgrade, Aleksinačkih Rudara 12-35, Belgrade, 11070, Serbia and Montenegro

    Ljubomir B. Ćirić

  2. Department of Applied Mathematics, Changwon National University, Changwon, 641-773, Korea

    Jeong S. Ume

  3. Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Belgrade, 11000, Serbia and Montenegro

    Siniša N. Ješić

Authors
  1. Ljubomir B. Ćirić
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  2. Jeong S. Ume
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  3. Siniša N. Ješić
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Correspondence to Ljubomir B. Ćirić.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ćirić, L.B., Ume, J.S. & Ješić, S.N. On random coincidence and fixed points for a pair of multivalued and single-valued mappings. J Inequal Appl 2006, 81045 (2006). https://doi.org/10.1155/JIA/2006/81045

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

Keywords

  • Measurable Mapping
  • Point Theorem
  • Measurable Space
  • Fixed Point Theorem
  • Polish Space