A best approximation theorem for nonexpansive set-valued mappings in hyperconvex metric spaces

DOI10.1216/rmjm/1181069628zbMath1097.54040OpenAlexW2009050661MaRDI QIDQ2495318

Jack T. Markin

Publication date: 5 July 2006

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069628

zbMATH Keywords

fixed point theoremshyperconvex metric spacesKy Fan best approximation theorem

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Selections in general topology (54C65) Fixed-point and coincidence theorems (topological aspects) (54H25) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items

Metric fixed point theory on hyperconvex spaces: recent progress, Best approximation and fixed point theorems in hyperconvex metric spaces, Best approximation theorems for nonexpansive and condensing mappings in hyperconvex spaces, Coincidence point, best approximation, and best proximity theorems for condensing set-valued maps in hyperconvex metric spaces, On coupled best proximity points and Ulam-Hyers stability

Cites Work

• Extension of uniformly continuous transformations and hyperconvex metric spaces
• KKM and Ky Fan theorems in hyperconvex metric spaces
• The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications
• Fixed point theorems in hyperconvex metric spaces
• Fixed point and selection theorems in hyperconvex spaces
• Hyperconvexity and Nonexpansive Multifunctions