Overview

This monograph focuses on geometric properties of Banach spaces and nonlinear iterations. The first half of the monograph (Chapters 1 to 5) develops materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained in each chapter are summarized at the end of the chapter for easy reference. The second half (Chapters 6 to 23) deals with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and most important results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings.

As a flourishing area of research for numerous mathematicians, there has been an explosion of research papers on these topics. This self-contained volume will be useful for graduate students of mathematical analysis, as well as being a vital text for mathematicians interested in learning about the subject and for specialists in nonlinear operator theory.

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9781848821934

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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. Cobza, Studia Universitatis Babe -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 Banacht

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