An abstract fixed point theorem for nonexpansive mappings
Author:
W. A. Kirk
Journal:
Proc. Amer. Math. Soc. 82 (1981), 640642
MSC:
Primary 54H25
MathSciNet review:
614894
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Abstract: A class of subsets of a bounded metric space is said to be normal if each member of contains a nondiametral point. An induction proof is given for the following. Suppose is a nonempty bounded metric space which contains a class of subsets which is countably compact, normal, stable under arbitrary intersections, and which contains the closed balls in . Then every nonexpansive selfmapping of has a fixed point.
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 , Mappings of generalized contractive type, J. Math. Anal. Appl. 32 (1970), 567572. MR 0271794 (42:6675)
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 , Asymptotic centers and nonexpansive mappings in some conjugate spaces, Pacific J. Math. (to appear).
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 J. P. Penot, Fixed point theorems without convexity, Analyse Non Convex (Pau, 1977), Bull. Soc. Math. France Mém. 60 (1979), 129152. MR 562261 (81c:47061)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198106148946
PII:
S 00029939(1981)06148946
Keywords:
Fixed point theorem,
nonexpansive mappings
Article copyright:
© Copyright 1981 American Mathematical Society
