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Fixed points of quasi-nonexpansive mappings

Published online by Cambridge University Press:  09 April 2009

W. G. Dotson Jr
W. G. Dotson Jr
Affiliation:
North Carolina State University at RaleighRaleigh, North Carolina.
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A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 2 , March 1972 , pp. 167 - 170
Copyright
Copyright © Australian Mathematical Society 1972

References

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