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Existence of Best Proximity Pairs and Equilibrium Pairs

Journal of Mathematical Analysis and Applications, 2006
Using Lassonde's fixed point theorem for Kakutani factorizable multifunctions, the authors prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies, which include previous fixed point theorems and equilibrium existence theorems.
Won Kyu Kim, Kyoung Hee Lee
exaly   +3 more sources

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, G Sankara Raju Kosuru
exaly   +4 more sources

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.
Sangho Kum
exaly   +2 more sources

Best Proximity Pair Theorems for Multifunctions With Open Fibres

Journal of Approximation Theory, 2000
Let \(A\) and \(B\) be non-empty subsets of a normed linear space \(E\), and let \(T:A\to 2^B\) be a convex multi-valued function with open fibres \(T^{-1}(y)\) (i.e.) \(\{x\in X:y\in Tx\}\). For an element \(x_0\in A\) sufficient conditions are found so that \(\text{dist}(x_0, Tx_0)= \text{dist}(A,B)\).
S Sadiq Basha, P Veeramani
exaly   +3 more sources

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.
Moosa Gabeleh, Hans-Peter Künzi
exaly   +3 more sources

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Proximinal Retracts and Best Proximity Pair Theorems

Numerical Functional Analysis and Optimization, 2003
Abstract This note is concerned with proximinality and best proximity pair theorems in hyperconvex metric spaces and in Hilbert spaces. Given two subsets A and B of a metric space and a mapping best proximity pair theorems provide sufficient conditions that ensure the existence of an such that Thus such theorems provide optimal approximate solutions in
Simeon Reich, P Veeramani
exaly   +2 more sources

Fuzzy Equilibrium via Best Proximity Pairs in Abstract Economies

Soft Computing, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Parin Chaipunya, Poom Kumam
exaly   +4 more sources

Best proximity pairs and equilibrium pairs for Kakutani multimaps

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Al-Thagafi, M. A., Shahzad, Naseer
openaire   +1 more source

Optimal problems of the best proximity pair by proximal normal structure

2023
Summary: Let \((A_1,A_2,A_3)\) be a triple of nonempty convex subsets of a metric space \(\Omega\). In this paper, we determine optimal problems of the best proximity pair by proximal normal structure between two sets \(A_1\) and \(A_2\) with the help of a third set \(A_3\) and we find some necessary and sufficient conditions for existence this optimal
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On best proximity pair theorems for relatively -continuous mappings

Nonlinear Analysis: Theory, Methods & Applications, 2011
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Eldred, A. Anthony, Raj, V. Sankar, Veeramani, P.   +2 more
openaire   +2 more sources