Some results on fixed points of multifunctions on abstract metric spaces. (English) Zbl 1217.54055

Radenović, Stojan; Kadelburg, Zoran

Math. Comput. Modelling 53, No. 5-6, 746-754 (2011).

Summary: Recently, H. E. Kunze, D. La Torre and E. R. Vrscay [J. Math. Anal. Appl. 330, No. 1, 159-173 (2007; Zbl 1115.47043)] proved some fixed point results for multifunctions in metric spaces. Sh. Rezapour and R. H. Haghi [Numer. Funct. Anal. Optim. 30, No. 7-8, 825–832 (2009; Zbl 1171.54033)] adapted these results to the case of abstract (cone) metric spaces when the underlying cone is normal with normal constant \(M=1\). The aim of this paper is to show that these results remain valid in the case when \(M>1\). Introducing new contraction conditions, our results generalize fixed point theorems of Covitz and Nadler, Kunze et al. and Rezapour and Haghi. An example is given to distinguish our results from the known ones. In addition, the case when two mappings are considered is treated.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54C60	Set-valued maps in general topology

Keywords:

cone metric space; normal cone; nonnormal cone; multifunctions; symmetric space

Citations:

Zbl 1115.47043; Zbl 1171.54033

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