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A
random fixed point theorem for a multivalued contraction
mapping
Shigeru Itoh |
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Vol. 68 (1977), No. 1, 85–90
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Abstract |
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Some results on measurability of multivalued mappings are given. Then using them, the following random fixed point theorem is proved; Theorem. Let X be a Polish space, (T,𝒜) a measurable space. Let F : T × X → CB(X) be a mapping such that for each x ∈ X, F(⋅,x) is measurable and for each t ∈ T, F(t,⋅) is k(t)-contraction, where k : T → [0,1) is measurable. Then there exists a measurable mapping u : T → X such that for every t ∈ T, u(t) ∈ F(t,u(t)). |
Mathematical Subject Classification 2000
Primary: 54H25
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Milestones
Received: 14 July 1976
Published: 1 January 1977
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Authors |
| Shigeru Itoh | |
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