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

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

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Let ( ) be ds durga hand soap 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 cocktail tree for sale 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.