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Best proximity points for asymptotic cyclic contraction mappings. (English) Zbl 1263.47065

The authors prove existence and convergence of unique best proximity points for asymptotic cyclic contractions in metric spaces satisfying the property UC and in uniformly convex Banach spaces. They also prove existence and convergence result for an asymptotic proximal pointwise contraction mapping in uniformly convex Banach spaces. Moreover, they prove existence of best proximity points for generalized cyclic contraction mappings in Banach spaces which do not necessarily satisfy the geometric property UC.

MSC:

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

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