Some results on Best Proximity Points for Cyclic Mappings

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Given A and B two subsets of a metric space, a mapping T : A∪B → A∪B is said to be cyclic if T (A) ⊆ B and T (B) ⊆ A. It is known that, if A and B are nonempty and complete and the cyclic map verifies for some k ∈ (0, 1) that d(Tx, Ty) ≤ kd(x, y) ∀ x ∈ A and y ∈ B, then A∩B 6= ∅ and the mapping T has a unique fixed point. A generalization of this situation was studied under the assumption of A ...

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ژورنال

عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin

سال: 2013

ISSN: 1370-1444

DOI: 10.36045/bbms/1378314516