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Zbl 1169.54023
Wardowski, Dariusz
Endpoints and fixed points of set-valued contractions in cone metric spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 1-2, A, 512-516 (2009). ISSN 0362-546X

{\it L.--G.\thinspace Huang} and {\it X.\,Zhang} [J.~Math.\ Anal.\ Appl.\ 332, No.\,2, 1468--1476 (2007; Zbl 1118.54022)] introduced the notion of cone metric space and established fixed point theorems for single-valued contractive maps in these spaces. In the paper under review, the author proves endpoint and fixed point theorems for set-valued contractive maps in cone metric spaces. Some examples are also given.
[Hemant Kumar Nashine (Raipur)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54F05 Ordered topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54C60 Set-valued maps
46B40 Ordered normed spaces

Keywords: fixed point; set-valued contraction; endpoint; ordered Banach space; cone metric space

Citations: Zbl 1118.54022

Cited in: Zbl 1246.54047 Zbl 1228.54041

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