Geometrical Background of Metric Fixed Point Theory

Stanisław Prus ()
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Stanisław Prus: Maria Curie-Sktodowski University, Department of Mathematics

Chapter Chapter 4 in Handbook of Metric Fixed Point Theory, 2001, pp 93-132 from Springer

Abstract: Abstract The interplay between the geometry of Banach spaces and fixed point theory has been very strong and fruitful. In particular, geometrical properties play key roles in metric fixed point problems. In this text we discuss the most basic of these geometrical properties. Since many fixed point results have a quantitative character, we place special emphasis on the scaling coefficients and functions corresponding to the properties considered. The material we cover is far from exhaustive, in particular we do not consider applications. These are treated elsewhere in the Handbook. The interested reader may also consult [5], [44] and [1].

Keywords: Banach Space; Fixed Point Theorem; Nonexpansive Mapping; Normal Structure; Fixed Point Theory (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-94-017-1748-9_4

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