Fixed point of multifunctions on cone metric spaces. (English) Zbl 1171.54033

Rezapour, Sh.; Haghi, R. H.

Numer. Funct. Anal. Optim. 30, No. 7-8, 825-832 (2009).

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

Citations:

Zbl 1118.54022; Zbl 1115.47043

References:

[1]	DOI: 10.1016/j.jmaa.2005.03.087 · Zbl 1118.54022
[2]	DOI: 10.1007/BF02771543 · Zbl 0192.59802
[3]	DOI: 10.1007/s101140200165 · Zbl 1027.47058
[4]	DOI: 10.1016/j.jmaa.2006.07.045 · Zbl 1115.47043
[5]	Mohebi H., Continuous Optimization, Current Trends and Modern Applications. Part II pp 343– (2005)
[6]	DOI: 10.1016/j.jmaa.2008.04.049 · Zbl 1145.54045