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Coincidence and common fixed points for generalized contraction multi-valued mappings. (English) Zbl 1221.47095
Summary: We prove the existence of coincidence and common fixed point theorems for generalized multi-valued $$f$$-contraction and generalized $$f$$-nonexpansive maps. In our results, we can drop the assumption of T-weakly commuting, which improves and extends the recent results of M. A. Al-Thagafi and N. Shahzad [Nonlinear Analysis 67, 2180–2188 (2007; Zbl 1125.47039)], N. Shahzed and N. Hussain [J. Math. Anal. Appl. 323, 1038–1046 (2006; Zbl 1107.47042)] and many other authors.

##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology 47H10 Fixed-point theorems