Geometric Properties of Banach Spaces and Nonlinear Iterations / by Charles Chidume.

Format:

Book

Author/Creator:

Chidume, Charles, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1965.

Lecture Notes in Mathematics, 0075-8434 ; 1965

Language:

English

Subjects (All):

Operator theory.

Global analysis (Mathematics).

Functional analysis.

Mathematical optimization.

Integral equations.

Numerical analysis.

Operator Theory.

Analysis.

Functional Analysis.

Calculus of Variations and Optimal Control; Optimization.

Integral Equations.

Numerical Analysis.

Local Subjects:

Operator Theory.

Analysis.

Functional Analysis.

Calculus of Variations and Optimal Control; Optimization.

Integral Equations.

Numerical Analysis.

Physical Description:

1 online resource (XVII, 326 pages).

Contained In:

Springer eBooks

Place of Publication:

London : Springer London, 2009.

System Details:

text file PDF

Summary:

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.

Contents:

Some Geometric Properties of Banach Spaces

Smooth Spaces

Duality Maps in Banach Spaces

Inequalities in Uniformly Convex Spaces

Inequalities in Uniformly Smooth Spaces

Iterative Method for Fixed Points of Nonexpansive Mappings

Hybrid Steepest Descent Method for Variational Inequalities

Iterative Methods for Zeros of ? - Accretive-Type Operators

Iteration Processes for Zeros of Generalized ? -Accretive Mappings

An Example; Mann Iteration for Strictly Pseudo-contractive Mappings

Approximation of Fixed Points of Lipschitz Pseudo-contractive Mappings

Generalized Lipschitz Accretive and Pseudo-contractive Mappings

Applications to Hammerstein Integral Equations

Iterative Methods for Some Generalizations of Nonexpansive Maps

Common Fixed Points for Finite Families of Nonexpansive Mappings

Common Fixed Points for Countable Families of Nonexpansive Mappings

Common Fixed Points for Families of Commuting Nonexpansive Mappings

Finite Families of Lipschitz Pseudo-contractive and Accretive Mappings

Generalized Lipschitz Pseudo-contractive and Accretive Mappings

Finite Families of Non-self Asymptotically Nonexpansive Mappings

Families of Total Asymptotically Nonexpansive Maps

Common Fixed Points for One-parameter Nonexpansive Semigroup

Single-valued Accretive Operators; Applications; Some Open Questions.

Other Format:

Printed edition:

ISBN:

9781848821903

Access Restriction:

Restricted for use by site license.