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Best Proximity Point Theorems for a Berinde MT-Cyclic Contraction on a Semisharp Proximal Pair [PDF]
International Journal of Mathematics and Mathematical Sciences, 2018 In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also
Chalongchai Klanarong +1 more
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Strong and weak convergence of Ishikawa iterations for best proximity pairs [PDF]
Open Mathematics, 2020 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.
Gabeleh Moosa +3 more
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t-Best Proximity Pair in Fuzzy Normed Spaces
Journal of Mathematical Extension, 2014 This study has considered the problem of finding best proximity pair in fuzzy metric spaces and uniformly convex fuzzy Banach spaces for fuzzy cyclic contraction map. We prove the uniqueness of this point in uniformly fuzzy Banach spaces. We also give
H. R. Khademzadeh, H. Mazaheri
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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 In 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 ...
Gabeleh Moosa, Künzi Hans-Peter A.
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Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps [PDF]
Fixed Point Theory and Applications, 2009 We 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 ð”„ðÂœκ-multimap or a multimap T:A→2B such that both T and S∘T are closed ...
Naseer Shahzad, M. A. Al-Thagafi
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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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BEST PROXIMITY PAIRS AND NASH EQUILIBRIUM PAIRS [PDF]
Journal of the Korean Mathematical Society, 2008 Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems.
Won-Kyu Kim, Sang-Ho Kum
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Bipartite graphs and best proximity pairs
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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Best proximity point (pair) results via MNC in Busemann convex metric spaces
Applied General Topology, 2022 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 spaces ...
Moosa Gabeleh, Pradip Ramesh Patle
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