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Endpoints and fixed points of set-valued contractions in cone metric spaces. (English) Zbl 1169.54023
L.–G. Huang and 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.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
54C60 Set-valued maps in general topology
46B40 Ordered normed spaces
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References:
[1] Deimling, K., Nonlinear functional analysis, (1985), Springer-Verlag · Zbl 0559.47040
[2] Feng, Y.; Liu, S., Fixed point theorems for multi-valued contractive maps and multi-valued Caristi type maps, J. math. anal. appl., 317, 103-112, (2006) · Zbl 1094.47049
[3] Huang, L.-G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive maps, J. math. anal. appl., 332, 1467-1475, (2007)
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