Introduction to Hyperconvex Spaces

R. Espínola () and M. A. Khamsi ()
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R. Espínola: Universidad de Sevilla, Departamento de Análisis Matemático Facultad dí Matemáticas
M. A. Khamsi: The University of Texas at El Paso, Department of Mathematical Sciences and Computer Science

Chapter Chapter 13 in Handbook of Metric Fixed Point Theory, 2001, pp 391-435 from Springer

Abstract: Abstract The notion of hyperconvexity is due to Aronszajn and Panitchpakdi [1] (1956) who proved that a hyperconvex space is a nonexpansive absolute retract, i.e. it is a non-expansive 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 [19, 29, 42, 46]). The nonlinear theory is still developing. The recent interest into these spaces goes back to the results of Sine [54] and Soardi [57] 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.

Keywords: Fixed Point Theorem; Nonexpansive Mapping; Multivalued Mapping; Common Fixed Point; Extremal Function (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-94-017-1748-9_13

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