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Fixed point of multifunctions on cone metric spaces. (English) Zbl 1171.54033
Summary: On a vector space, one can define an order by using a cone in the vector space. In this way, L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] reviewed cone metric spaces as a generalization of metric spaces with a different view. Most known cones are normal with normal constant $$M=1$$. In this paper, we give some results about fixed point of multifunctions on the cone metric spaces with normal constant $$M = 1$$. In this way, we provide a generalization of the main results of H. E. Kunze, D. La Torre and E. R. Vrscay [J. Math. Anal. Appl. 330, No. 1, 159–173 (2007; Zbl 1115.47043)].

##### 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 47H04 Set-valued operators
##### Keywords:
cone metric space; cone topology; fixed point; multifunction
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##### References:
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