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Erschienen in:
Open Access 01.12.2006 | Research Article
On random coincidence and fixed points for a pair of multivalued and single-valued mappings
Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006
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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.
) 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.