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Introduction to Hyperconvex Spaces

In: Handbook of Metric Fixed Point Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • R. Espínola & M. A. Khamsi, 2001. "Introduction to Hyperconvex Spaces," Springer Books, in: William A. Kirk & Brailey Sims (ed.), Handbook of Metric Fixed Point Theory, chapter 0, pages 391-435, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1748-9_13
    DOI: 10.1007/978-94-017-1748-9_13
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