Measures of Noncompactness in Metric Fixed Point Theory

1. Front Matter

   Pages i-vii

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2. Introduction

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 1-4

3. The Fixed Point Theorems of Brouwer and Schauder

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 5-16

4. Measures of Noncompactness

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 17-44

5. Minimal Sets for a Measure of Noncompactness

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 45-56

6. Convexity and Smoothness

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 57-84

7. Nearly Uniform Convexity and Nearly Uniform Smoothness

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 85-108

8. Fixed Points for Nonexpansive Mappings and Normal Structure

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 109-130

9. Fixed Point Theorems in the Absence of Normal Structure

   • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

   Pages 131-140

10. Uniformly Lipschitzian Mappings

    • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

    Pages 141-152

11. Asymptotically Regular Mappings

    • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

    Pages 153-166

12. Packing Rates and ø-Contractiveness Constants

    • J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

    Pages 167-195

13. Back Matter

    Pages 197-216

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What is clear and easy to grasp attracts us; complications deter David Hilbert The material presented in this volume is based on discussions conducted in peri­ odically held seminars by the Nonlinear Functional Analysis research group of the University of Seville. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Special em­ phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see [AKPRSj, [BG]) or in books on metric fixed point theory (see [GK1], [Sm], [Z]). Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. However, as in any work of this type, an effort has been made to revise many proofs and to place many others in a correct setting. Our research was made possible by partial support of the D.G.I.C.y'T. and the Junta de Andalucia.

• Differential equations
• Nonlinear analysis
• calculus
• compactness
• fixed point theory
• function
• functional analysis
• proof

• Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

  J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo

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