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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

Citations:

Zbl 1118.54022
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Full Text: DOI

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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.