Ultra-Methods in Metric Fixed Point Theory

M. A. Khamsi () and B. Sims ()
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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

Chapter Chapter 6 in Handbook of Metric Fixed Point Theory, 2001, pp 177-199 from Springer

Abstract: 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].

Keywords: Banach Space; Convex Subset; Nonexpansive Mapping; Banach Lattice; Fixed Point Theory (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-1748-9_6

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DOI: 10.1007/978-94-017-1748-9_6

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