This monograph focuses on geometric properties of Banach spaces and nonlineariterations. 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-typemappings. 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. Self-contained, with detailed motivations, explanations and examples In-depth, comprehensive and up-to-date coverage Contains interesting, important and reasonable open problems Summaries of key inequalities and theorems for easy reference INDICE: From the contents 1. Geometric Properties.- 2. Smooth Spaces.- 3.Duality Maps in Banach Spaces.- 4.Inequalities in Uniformly Convex Spaces.- 5. Inequalities in Uniformly Smooth Spaces.- 6. Iterative Method for Fixed Pointsof Nonexpansive Mappings.- 7. Hybrid Steepest Descent Method for Variational Inequalities.- 8. Iterative Methods for Zeros of (phi)-Accretive-Type Operators.- 9. Iteration Processes for Zeros of Generalized (phi)-Accretive Mappings.-10. An Example; Mann Iteration for Strictly Pseudo-contractive Mappings.- 11.Approximation of Fixed Points of Lipschitz Pseduo-contractive Mappings.- 12. Generalized Lipschitz Accretive and Pseudo-contractive Mappings.- 13. Applications to Hammerstein Integral Equations.- 14. Iterative Methods for Some Generalizations of Nonexpansive Maps.- 15. Common Fixed Points for Finite Families of Nonexpansive Mappings.- 16. Common Fixed Points for Countable Families of Nonexpansive Mappings.- 17. Common Fixed Points for Families of Commuting Nonexpansive Mappings.
- ISBN: 978-1-84882-189-7
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 335
- Fecha Publicación: 01/01/2009
- Nº Volúmenes: 1
- Idioma: Inglés