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On random approximations and a random fixed point theorem for set valued mappings. (English) Zbl 0607.47057

A random fixed point result for set-valued mappings with compact convex values is stated and proved. The obtained theorem is shown to contain a previous one due to A. T. Bharucha-Reid and A. Mukherjea [Bull. Am. Math. Soc. 82, 641-657 (1976; Zbl 0339.60061)].
Reviewer: M.Turinici

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
60H25 Random operators and equations (aspects of stochastic analysis)

Citations:

Zbl 0339.60061
Full Text: DOI

References:

[1] A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), no. 5, 641 – 657. · Zbl 0339.60061
[2] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53 – 72. · Zbl 0296.28003
[3] Shigeru Itoh, Random fixed-point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), no. 2, 261 – 273. · Zbl 0407.60069 · doi:10.1016/0022-247X(79)90023-4
[4] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 397 – 403 (English, with Russian summary). · Zbl 0152.21403
[5] Simeon Reich, Fixed points in locally convex spaces, Math. Z. 125 (1972), 17 – 31. · Zbl 0216.17302 · doi:10.1007/BF01111112
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