A fixed point theorem for asymptotically nonexpansive mappings
Authors:
K. Goebel and W. A. Kirk
Journal:
Proc. Amer. Math. Soc. 35 (1972), 171174
MSC:
Primary 47H10
MathSciNet review:
0298500
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Abstract: Let K be a subset of a Banach space X. A mapping is said to be asymptotically nonexpansive if there exists a sequence of real numbers with as such that . It is proved that if K is a nonempty, closed, convex, and bounded subset of a uniformly convex Banach space, and if is asymptotically nonexpansive, then F has a fixed point. This result generalizes a fixed point theorem for nonexpansive mappings proved independently by F. E. Browder, D. Göhde, and W. A. Kirk.
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 , On nonlinear mappings of strongly semicontractive type, J. Math. Anal. Appl. 27 (1969), 409412. MR 39 #6128. MR 0244814 (39:6128)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197202985003
PII:
S 00029939(1972)02985003
Keywords:
Fixed point theorem,
nonexpansive mapping,
asymptotically nonexpansive mapping,
uniformly convex Banach space,
lipschitzian mapping
Article copyright:
© Copyright 1972
American Mathematical Society
