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Common fixed point results in CAT(0) spaces. (English) Zbl 1269.54018
Summary: Let X be a complete CAT(0) space, T be a generalized multivalued nonexpansive mapping, and t be a single valued quasi-nonexpansive mapping. Under the assumption that T and t commute weakly, we shall prove the existence of a common fixed point for them. In this way, we extend and improve a number of recent results obtained by N. Shahzad [Topology Appl. 156, No. 5, 997–1001 (2009; Zbl 1175.47049); Nonlinear Anal., Theory Methods Appl. 70, No. 12, A, 4338–4340 (2009; Zbl 1167.47042)], N. Shahzad and J. Markin [J. Math. Anal. Appl. 337, No. 2, 1457–1464 (2008; Zbl 1137.47043)], and S. Dhompongsa et al. [J. Math. Anal. Appl. 312, No. 2, 478–487 (2005; Zbl 1086.47019)].

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
54E50Complete metric spaces
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