Random approximations and random fixed point theorems for non-self-maps. (English) Zbl 0676.47041

Lin, Tzu-Chu

Proc. Am. Math. Soc. 103, No. 4, 1129-1135 (1988).

The author proves several theorems containing stochastic versions of a theorem of Ky Fan [Math. Z. 112, 234-240 (1969; Zbl 0185.395)] for random operations f: \(\Omega\) \(\times S\to X\) where S is a closed ball in a separable Banach space (or closed convex subset of a separable Hilbert space) and \(\Omega\) is a measurable space. He obtains some stochastic fixed point theorems as applications of general results.

Reviewer: M.Sablik

MSC:

47H10	Fixed-point theorems
60H25	Random operators and equations (aspects of stochastic analysis)
41A50	Best approximation, Chebyshev systems

Keywords:

stochastic versions of a theorem of Ky Fan; random mapping; random fixed point; stochastic fixed point theorems

Citations:

Zbl 0185.395

References:

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