Common best proximity pairs via the concept of complete proximal normal structure

DOI10.1007/s43034-020-00057-xzbMath1498.47102OpenAlexW3007149964MaRDI QIDQ781725

Moosa Gabeleh, Jack T. Markin

Publication date: 17 July 2020

Published in: Annals of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s43034-020-00057-x

zbMATH Keywords

uniformly convex Banach spacerelatively nonexpansive mappingbest proximity paircomplete proximal normal structure

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) Programming in abstract spaces (90C48) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

• Existence and convergence of best proximity points
• Convergence of Picard's iteration using projection algorithm for noncyclic contractions
• Pythagorean property and best-proximity point theorems
• Fixed point theorems and convergence theorems for some generalized nonexpansive mappings
• Fixed-point theorems for families of contraction mappings
• Nonexpansive mappings and fixed-points in Banach spaces
• On the Structure of Minimal Sets of Relatively Nonexpansive Mappings
• Iteration processes for nonexpansive mappings
• A new approach to relatively nonexpansive mappings
• Characterizations of Normal Structure
• An Introduction to Metric Spaces and Fixed Point Theory
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Proximal normal structure and relatively nonexpansive mappings
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