Let be a metric space, then a function is called a -distance on [O. Kada, T. Suzuki and W. Takahashi, Math. Jap. 44, 381-391 (1996; Zbl 0897.54029)] if: (1) for all , ; (2) for any , is lower semicontinuous; (3) for any , there exists such that and imply . For any and we denote by and by and is a nonempty closed susbset of and .
Recently, J.-S. Ume [J. Math. Anal. Appl. 225, 630-640 (1998; Zbl 0917.54047)] improved some fixed points theorem in a complete metric space using the concept of -distance. In the paper under review the authors, using this concept, prove some common fixed point theorems for two multivalued mappings and in a complete metric space.
The main result of this paper is the following theorem: Let be a complete metric space with a metric and let be a -distance on . Suppose that and are two mappings of into and is a mapping such that , for all nonempty subsets of , , , , , , , and some with , , , , for every with or , where means . Then and have a common fixed point.