Lecture Notes in Mathematics

Geometric Properties of Banach Spaces and Nonlinear Iterations

Authors: Chidume, Charles

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  • Is a self-contained monograph with detailed motivations, explanations, and examples
  • Offers in-depth, comprehensive and up-to-date coverage
  • Contains interesting, important, and reasonable open problems
  • Provides summaries of key inequalities and theorems for easy reference
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About this book

Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years.

Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings.

Carefully referenced and full of recent, incisive findings and interesting open-questions, this volume will prove useful for graduate students of mathematical analysis and will be a key-read for mathematicians with an interest in applications of geometric properties of Banach spaces, as well as specialists in nonlinear operator theory.

Reviews

From the reviews: “The aim of the present book is to give an introduction to this very active area of investigation. … the book is of great help for graduate and postgraduate students, as well as for researchers interested in fixed point theory, geometry of Banach spaces and numerical solution of various kinds of equations - operator differential equations, differential inclusions, variational inequalities.” (S. Cobzaş, Studia Universitatis Babeş-Bolyai. Mathematica, Vol. LIV (4), December, 2009) “The topic of this monograph falls within the area of nonlinear functional analysis. … The main purpose of this book is to expose in depth the most important results on iterative algorithms for approximation of fixed points or zeroes of the mappings mentioned above. … this book picks up the most important results in the area, its explanations are comprehensive and interesting and I think that this book will be useful for mathematicians interested in iterations for nonlinear operators defined in Banach spaces.” (Jesus Garcia-Falset, Mathematical Reviews, Issue 2010 f)

Table of contents (23 chapters)

Table of contents (23 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-84882-190-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-1-84882-189-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Properties of Banach Spaces and Nonlinear Iterations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1965
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84882-190-3
DOI
10.1007/978-1-84882-190-3
Softcover ISBN
978-1-84882-189-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVII, 326
Topics