On best proximity points for pseudocontractions in the intermediate sense for non-cyclic and cyclic self-mappings in metric spaces
نویسندگان
چکیده
منابع مشابه
Coincidence Quasi-Best Proximity Points for Quasi-Cyclic-Noncyclic Mappings in Convex Metric Spaces
We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...
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Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...
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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: Fixed Point Theory and Applications
سال: 2013
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2013-146