On some nonself mappings

Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ∂K (∂K the boundary of K) into K then T has a unique fixed point in K.

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Bibliographic Details
Published in:Mathematische Nachrichten 2003-03, Vol.251 (1), p.28-33
Main Authors: Ćirić, LJ. B., Ume, J. S., Khan, M. S., Pathak, H. K.
Format: Article
Language:English
Subjects:
Banach space
Banach space, nonself–mapping, fixed point
fixed point
nonself-mapping
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Summary:Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ∂K (∂K the boundary of K) into K then T has a unique fixed point in K.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200310028