Relative Continuity, Proximal Boundedness and Best Proximity Point Theorems

DOI10.1080/01630563.2022.2041659OpenAlexW4214519843WikidataQ113851617 ScholiaQ113851617MaRDI QIDQ5078216

Naseer Shahzad, S. Sadiq Basha, K. Sethukumarasamy

Publication date: 23 May 2022

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2022.2041659

zbMATH Keywords

fixed pointbest proximity pointcyclic mappingrelative continuitybest proximal completenessproximal boundedness

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

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• Common best proximity point theorems: global minimization of some real-valued multi-objective functions
• On best proximity pair theorems for relatively \(u\)-continuous mappings
• Best proximity point theorems generalizing the contraction principle
• Best proximity points: Optimal solutions
• Best proximity point theorems for contractive mappings
• The existence of best proximity points in metric spaces with the property UC
• Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces
• Convergence and existence results for best proximity points
• Convergence of Picard's iteration using projection algorithm for noncyclic contractions
• Best proximity point theorems for proximal cyclic contractions
• Best proximity point theorems for some classes of contractions
• Best proximity pair theorems for multifunctions with open fibres
• Pythagorean property and best-proximity point theorems
• Existence of the solution to variational inequality, optimization problem, and elliptic boundary value problem through revisited best proximity point results
• Best proximity points for cyclic Meir-Keeler contractions
• Best proximity pairs and equilibrium pairs for Kakutani multimaps
• Proximinal Retracts and Best Proximity Pair Theorems

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