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Some random approximations and random fixed point theorems for 1-set-contractive random operators. (English) Zbl 0869.47031

Summary: We prove that the random version of Ky Fan’s Theorem [Math. Z. 112, 234-240 (1969; Zbl 0185.39503)] is true for 1-set-contractive random operators \(f: \Omega \times B_R\rightarrow X \), where \(B_R\) is a weakly compact separable closed ball in a Banach space \(X\) and \(\Omega\) is a measurable space. This class of 1-set-contractive random operators includes condensing random operators, semicontractive random operators, LANE random operators, nonexpansive random operators and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions.

MSC:

47H10 Fixed-point theorems
60H25 Random operators and equations (aspects of stochastic analysis)
41A50 Best approximation, Chebyshev systems
47H40 Random nonlinear operators

Citations:

Zbl 0185.39503
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References:

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