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Some random approximations
and random fixed point theorems
for 1-set-contractive random operators


Author: Liu Li-Shan
Journal: Proc. Amer. Math. Soc. 125 (1997), 515-521
MSC (1991): Primary 47H10, 60H25; Secondary 41A50
MathSciNet review: 1350953
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Abstract: In this paper, we will prove that the random version of Fan's Theorem (Math. Z. 112 (1969), 234-240) is true for 1-set-contractive random operator $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 operator 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.


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Additional Information

Liu Li-Shan
Affiliation: Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-97-03589-2
Keywords: Random approximations and random fixed point theorems, 1-set-contractive random operator, semicontractive random operator, LANE random operators
Received by editor(s): August 30, 1994
Received by editor(s) in revised form: August 22, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society