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; iterative approximation of: zeros of accretive-type operators; solutions of variational inequality problems; solutions of Hammerstein integral equations; and common fixed points (and common zeros) of families of nonlinear mappings.

As a flourishing area of research for numerous mathematicians, there has been an explosion of research papers on these topics. In this monograph, some recent incisive findings and interesting, important open questions are included. 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.