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A fixed point theorem for a family of nonexpansive mappings

Published online by Cambridge University Press:  17 April 2009

V.M. Sehgal
V.M. Sehgal
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA.
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Abstract

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Let E be a separated, locally convex topological vector space and F a commutative family of nonexpansive mappings defined on a quasi-complete convex (not necessarily bounded) subset X of E. In this paper, it is proved that if one of the mappings in F is condensing with a bounded range then the family F has a common fixed point in X. This result improves several well-known results and supplements a recent result of E. Tarafdar (Bull. Austral. Math. Soc. 13 (1975), 241–254) for such mappings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 111 - 116
Copyright
Copyright © Australian Mathematical Society 1976

References

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