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)
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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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