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On the Approximation of Fixed Points of Locally Nonexpansive Mappings

Published online by Cambridge University Press:  20 November 2018

W. A. Kirk  and
Claudio Morales
W. A. Kirk
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Claudio Morales
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
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Abstract

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It is shown that techniques of Browder and Ishikawa for approximating fixed points of nonexpansive mappings extend in a more restricted sense to the locally nonexpansive case.

Keywords

47H10Locally nonexpansive mappingfixed point
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 441 - 445
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Browder, F. E., Convergence of approximants to fixed points of non-expansive nonlinear maps in Banach spaces, Arch. Rational Mech. Anal. 24 (1967), 82-90.Google Scholar
2. Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665.Google Scholar
3. Gôhde, D., Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251-258.Google Scholar
4. Halpern, B., Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73 (1967), 957-961.Google Scholar
5. Ishikawa, S., Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71.Google Scholar
6. Kirk, W. A., A fixed point theorem for local pseudo-contractions in uniformly convex spaces, Manuscripta Math. 30 (1979), 89-102.Google Scholar
7. Kirk, W. A. and Morales, C., Fixed point theorems for local strong pseudo-contractions, J. Nonlinear Analysi. 4 (1980), 363-368.Google Scholar
8. Morales, C., On the fixed point theory for local k-pseudo-contractions, Proc. Amer. Math. Soc. 81 (1981), 71-74.Google Scholar