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Some random approximations and random fixed point theorems for 1-set-contractive random operators
Author(s):
Liu
Li-Shan
Journal:
Proc. Amer. Math. Soc.
125
(1997),
515-521.
MSC (1991):
Primary 47H10, 60H25;
Secondary 41A50
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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  , where  is a weakly compact separable closed ball in a Banach space  and  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:
10.1090/S0002-9939-97-03589-2
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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