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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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Corrigendum to the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings” [PDF]
Demonstratio Mathematica, 2021 The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings,” Demonstr.
Gabeleh Moosa
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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.
Slah Sahmim +2 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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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.
S. A. M. Mohsenalhosseini +2 more
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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.
Samih Lazaiz +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, Fisicas Y Naturales - Serie A: Matematicas, 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 Theorems for Continuous Set-Valued Maps [PDF]
Fixed Point Theory and Applications, 2008 A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces.
R. P. Agarwal +3 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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Some results on best proximity pair theorems
Applied General Topology, 2002 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 linear ...
P.S. Srinivasan, P. Veeramani
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