Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topological Fixed Point Theory and Its Applications, Band 6) - Softcover

Agarwal, Ravi P.; O'Regan, Donal; Sahu, D. R.

Softcover

ISBN 10: 1441926062 ISBN 13: 9781441926067

Verlag: Springer, 2010

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Erdal Karapinar, Ph.D., is a Professor in the Department of Mathematics at Cankaya University and Visiting Professor at the China Medical University of Taichung. He completed his Ph.D. at the Middle East Technical University (METU), Turkiye. He is the co-author of one book, more than 10 chapters for edited books, and more than 400 research articles in peer-reviewed journals. His research interests include functional analysis and metric fixed point theory. Ravi P. Agarwal, Ph.D., is a Professor in the Department of Mathematics at the Texas A&M University-Kingsville. He completed his Ph.D. at the Indian Institute of Technology, Madras, India, in 1973. Dr. Agarwal has authored or co-authored 50 books and 1,750 research articles. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 1441926062
• ISBN 13: 9781441926067
• Einband: Taschenbuch
• Anzahl der Seiten: 380
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland