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Approximate Best Proximity Pairs in Metric Space [PDF]
Abstract and Applied Analysis, 2011 Let A and B be nonempty subsets of a metric space X and also T : A ∪ B → A ∪ B and T(A)⊆B, T(B)⊆A. We are going to consider element x ∈ A such that d(x, Tx) ≤ d(A, B) + ϵ for some ϵ > 0. We call pair (A, B) an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, T ...
Mohsenalhosseini, S. A. M. +2 more
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Best Proximity Pairs Theorems for Continuous Set-Valued Maps [PDF]
Fixed Point Theory and Applications, 2008 AbstractA best proximity pair for a set-valued map "Equation missing" with respect to a set-valued map "Equation missing" is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem.
Amini-Harandi, A +3 more
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Some results on best proximity pair theorems
Applied General Topology, 2002 <p>Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element x<sub>o</sub> ϵ A, such that</p> <p>d(x<sub>o</sub>; T x<sub>o</sub>) = d(A;B)</p> <p>where T : A 2<sup>B</sup> is a multifunction defined on suitable ...
Srinivasan, P.S., Veeramani, P.
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Convergence and Best Proximity Points for Generalized Contraction Pairs [PDF]
Mathematics, 2019 This paper is devoted to studying the existence of best proximity points and convergence for a class of generalized contraction pairs by using the concept of proximally-complete pairs and proximally-complete semi-sharp proximinal pairs. The obtained results are generalizations of the result of Sadiq Basha (Basha, S., Best proximity points: global ...
Slah Sahmim +2 more
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Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings [PDF]
Demonstratio Mathematica, 2020 AbstractIn this study, at first we prove that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces by using the projection operator.
Gabeleh Moosa, Künzi Hans-Peter A.
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Strong and weak convergence of Ishikawa iterations for best proximity pairs [PDF]
Open Mathematics, 2020 Abstract Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be a noncyclic relatively nonexpansive mapping if T(A) ⊆ A, T(B) ⊆ B and ∥Tx − Ty∥ ≤ ∥x − y∥ for all (x, y) ∈ A × B. A best proximity pair for such a mapping T is a point (p, q) ∈ A × B such that p = Tp, q = Tq and d(p, q) = dist(A,
Gabeleh Moosa +3 more
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Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps [PDF]
Fixed Point Theory and Applications, 2008 AbstractWe establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an "Equation missing"-multimap or a multimap "Equation missing" such that both "Equation missing" and "Equation missing" are closed and have the KKM property for each Kakutani multimap ...
Naseer Shahzad, M. A. Al-Thagafi
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Noncyclic Meir-Keeler contractions and best proximity pair theorems
Demonstratio Mathematica, 2018 Abstract In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and ...
Gabeleh Moosa, Markin Jack
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Best Proximity Pairs in Ultrametric Spaces [PDF]
p-Adic Numbers, Ultrametric Analysis and Applications, 2021 In the present paper, we study the existence of best proximity pairs in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair $(A,B)$ has a best proximity pair. As a consequence we generalize a well known best approximation result and we derive some fixed point theorems.
Chaira, Karim +2 more
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A characterization of weak proximal normal structure and best proximity pairs [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022 The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of weak proximal normal structure using best proximity pair property.
Abhik Digar +2 more
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