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Ultra-Methods in Metric Fixed Point Theory

In: Handbook of Metric Fixed Point Theory

Author

Listed:
  • M. A. Khamsi

    (The University of Texas at El Paso, Department of Mathematical Sciences and Computer Science)

  • B. Sims

    (The University of Newcastle, Mathematics, School of Mathematical and Physical Sciences)

Abstract

Over the last two decades ultrapower techniques have become major tools for the development and understanding of metric fixed point theory. In this short chapter we develop the Banach space ultrapower and initiate its use in studying the weak fixed point property for nonexpansive mappings. For a more extensive and detailed treatment than is given here the reader is referred to [1] and [21].

Suggested Citation

  • M. A. Khamsi & B. Sims, 2001. "Ultra-Methods in Metric Fixed Point Theory," Springer Books, in: William A. Kirk & Brailey Sims (ed.), Handbook of Metric Fixed Point Theory, chapter 0, pages 177-199, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1748-9_6
    DOI: 10.1007/978-94-017-1748-9_6
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