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Common fixed point results with applications in convex metric space. (English) Zbl 1152.54029

In this paper the author studies common fixed point theorems for a class of mappings and applies these results to convex metric spaces. Precisely he obtains results showing existence of common fixed points for \(C_q\)-commuting maps which are more general than weakly compatible maps, in the settings of a convex metric space. Applying uniformly \(C_q\)-commuting maps to asymptotically \(S\)-nonexpansive mappings, common fixed point theorems are proved. Finally he obtains results on the best approximation as a fixed point of uniformly \(C_q\)-commuting mappings and \(C_q\)-commuting in a convex metric space.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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