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Endpoints and fixed points of set-valued contractions in cone metric spaces. (English) Zbl 1169.54023
{\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.

54H25Fixed-point and coincidence theorems in topological spaces
54F05Linearly, generalized, and partial ordered topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
54C60Set-valued maps (general topology)
46B40Ordered normed spaces
Full Text: DOI
[1] Deimling, K.: Nonlinear functional analysis. (1985) · 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)