Best proximity point theorems for rational proximal contractions

DOI10.1186/1687-1812-2013-95zbMath1295.41038OpenAlexW2159812168WikidataQ59292904 ScholiaQ59292904MaRDI QIDQ2249124

Calogero Vetro, Poom Kumam, Hemant Kumar Nashine

Publication date: 8 July 2014

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2013-95

zbMATH Keywords

contractionfixed pointbest proximity pointoptimal approximate solutiongeneralized proximal contraction

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

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Cites Work

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• Best proximity point theorems for generalized proximal contractions
• Coupled best proximity point theorem in metric spaces
• Some common best proximity points for proximity commuting mappings
• Best proximity points: Global optimal approximate solutions
• Common best proximity points: Global optimal solutions
• Existence and convergence of best proximity points
• The existence of best proximity points in metric spaces with the property UC
• Erratum to: ``Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces [Nonlinear Anal. (2008), doi: 10.1016/j.na.2008.04.037]
• Best proximity points: convergence and existence theorems for \(p\)-cyclic mappings
• Best proximity sets and equilibrium pairs for a finite family of multimaps
• Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces
• Convergence and existence results for best proximity points
• Best proximity point theorems for \(p\)-cyclic Meir--Keeler contractions
• Proximal pointwise contraction
• Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces
• Approximate selections, best approximations, fixed points, and invariant sets
• Generalized proximal \(\psi\)-contraction mappings and best proximity points
• Best proximity point theorems for generalized cyclic contractions in ordered metric spaces
• Best proximity pair theorems for multifunctions with open fibres
• Best proximity points for cyclic Meir-Keeler contractions
• Common best proximity points: global optimization of multi-objective functions
• On general best proximity pairs and equilibrium pairs in free abstract economies
• Best proximity pairs and equilibrium pairs for Kakutani multimaps
• Extensions of two fixed point theorems of F. E. Browder
• Best proximity points for generalized proximal \(C\)-contraction mappings in metric spaces with partial orders
• Best proximity pair theorems for relatively nonexpansive mappings
• Mathematical Model for Waste Reduction in Aluminum Fabrication Industry in Kuwait
• Extensions of Banach's Contraction Principle
• Fixed-point theorems for set-valued mappings and existence of best approximants
• A theorem on best approximations
• A Generalization to Multifunctions of Fan's Best Approximation Theorem
• Some extensions of fan's best approximation theorem
• Proximinal Retracts and Best Proximity Pair Theorems
• Asymptotic expansions for a model with distinguished “fast” and “slow” variables, described by a system of singularly perturbed stochastic differential equations
• Proximal normal structure and relatively nonexpansive mappings
• Best proximity pair theorems

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