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Fixed Point Theory for Lipschitzian-type Mappings with Applications

Buch | Hardcover
368 Seiten
2009
Springer-Verlag New York Inc.
978-0-387-75817-6 (ISBN)

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Fixed Point Theory for Lipschitzian-type Mappings with Applications - Ravi P. Agarwal, Donal O'Regan, D. R. Sahu
CHF 224,65 inkl. MwSt
In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis.


This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields.


This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Fundamentals.- Convexity, Smoothness, and Duality Mappings.- Geometric Coefficients of Banach Spaces.- Existence Theorems in Metric Spaces.- Existence Theorems in Banach Spaces.- Approximation of Fixed Points.- Strong Convergence Theorems.- Applications of Fixed Point Theorems.

From the reviews:

“The present book explains many of the basic techniques and … the classical results of fixed point theory, and normal structure properties. … Exercises are included in each chapter. As such, it is a self-contained book that can be used in a course for graduate students.” (Srinivasa Swaminathan, Zentralblatt MATH, Vol. 1176, 2010)

“This book provides a presentation of fixed point theory for Lipschitzian type mappings in metric and Banach spaces. … An exercise section is included at the end of each chapter, containing interesting and well chosen material in order to cover topics complementing the main body of the text. … It is worthwhile to point out that a beginner in this area is certainly well served with this text … . A book including all … topics together for sure should be welcomed for graduate students.” (Enrique Llorens-Fuster, Mathematical Reviews, Issue 2010 e)

Reihe/Serie Topological Fixed Point Theory and Its Applications ; 6
Zusatzinfo X, 368 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-387-75817-8 / 0387758178
ISBN-13 978-0-387-75817-6 / 9780387758176
Zustand Neuware
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