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Some results on best proximity pair theorems [PDF]
Applied General Topology, 2002 [EN] Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element xo ϵ A, such that d(xo; T xo) = d(A;B) where T : A 2B is a multifunction defined on suitable subsets A and B of a normed ...
Srinivasan, P.S., Veeramani, P.
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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.
H. Mazaheri +2 more
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Best proximity pair results for relatively nonexpansive mappings in geodesic spaces [PDF]
Numerical Functional Analysis and Optimization, 2013 Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \cup B \rightarrow A \cup B$ is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A, y\in B.$ A best proximity point for such a mapping is a point $x \in A ...
Leon, Aurora Fernandez, Nicolae, Adriana
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Best proximity point (pair) results via MNC in Busemann convex metric spaces [PDF]
Applied General Topology, 2022 [EN] In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex ...
Gabeleh, Moosa, Patle, Pradip Ramesh
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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.
Oleksiy Dovgoshey +2 more
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Bipartite graphs and best proximity pairs [PDF]
Ukrainian Mathematical Bulletin, 2022 We say that a bipartite graph $G(A, B)$ with fixed parts $A$, $B$ is proximinal if there is a semimetric space $(X, d)$ such that $A$ and $B$ are disjoint proximinal subsets of $X$ and all edges $\{a, b\}$ satisfy the equality $d(a, b) = \operatorname{dist}(A, B)$. It is proved that a bipartite graph $G$ is not isomorphic to any proximinal graph iff $G$
Chaira, Karim +2 more
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On a new variant of F-contractive mappings with application to fractional differential equations [PDF]
Nonlinear Analysis, 2022 The present article intends to prove the existence of best proximity points (pairs) using the notion of measure of noncompactness. We introduce generalized classes of cyclic (noncyclic) F-contractive operators, and then derive best proximity point (pair)
Gabeleh, Moosa, Patlea, Pradip Ramesh
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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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On selections of the metric projection and best proximity pairs in hyperconvex spaces [PDF]
, 2005 In this work we present new results on nonexpansive retractions and best proximity pairs in hyperconvex metric spaces. We sharpen the main results of R. Esp´ınola et al. in [3] (Nonexpansive retracts in hyperconvex spaces, J. Math. Anal. Appl. 251 (2000)
Espínola García, Rafael
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Best Proximity Pair Theorems for Noncyclic Mappings in Banach and Metric Spaces [PDF]
, 2016 Let A and B be two nonempty subsets of a metric space X. A mapping T : A[B ! A[B is said to be noncyclic if T(A) A and T(B) B. For such a mapping, a pair (x; y) 2 A B such that Tx = x, Ty = y and d(x; y) = dist(A;B) is called a best proximity ...
Fernández León, Aurora, Gabeleh, M.
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