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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 {\it 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)], {\it N. Shahzad} and {\it J. Markin} [J. Math. Anal. Appl. 337, No. 2, 1457--1464 (2008; Zbl 1137.47043)], and {\it S. Dhompongsa} et al. [J. Math. Anal. Appl. 312, No. 2, 478--487 (2005; Zbl 1086.47019)].

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