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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)
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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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