Opened Access Introduction to hyperconvex spaces

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Author: Espínola García, Rafael
Khamsi, Mohamed Amine
Coordinator/Director: Kirk, William Art
Sims, Brailey
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2001
Published in: Handbook of Metric Fixed Point Theory
ISBN/ISSN: 9789048157334
Document type: Chapter of Book
Abstract: The notion of hyperconvexity is due to Aronszajn and Panitchpakdi (1956) who proved that a hyperconvex space is a nonexpansive absolute retract, i.e. it is a nonexpansive retract of any metric space in which it is isometrically embedded. The corresponding linear theory is well developed and associated with the names of Gleason, Goodner, Kelley and Nachbin (see for instance. The nonlinear theory is still developing. The recent interest into these spaces goes back to the results of Sine and Soardi who proved independently that fixed point property for nonexpansive mappings holds in bounded hyperconvex spaces. Since then many interesting results have been shown to hold in hyperconvex spaces.
Cite: Espínola García, R., y Khamsi, M.A. (2001). Introduction to hyperconvex spaces. En B. Sims, W.A. Kirk (Ed.), Handbook of Metric Fixed Point Theory (pp. 391-435). Dordrecht: Springer
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DOI: 10.1007/978-94-017-1748-9_13

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