rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Geometric Properties of Banach Spaces and Nonlinear Iterations
  name:
    name part: Chidume, Charles.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxk
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 326 p. online resource.
  abstract: 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.
  table of 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.
  note: by Charles Chidume.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Functional analysis
  subject:
    topic: Integral equations
  subject:
    topic: Operator theory
  subject:
    topic: Numerical analysis
  subject:
    topic: Calculus of variations
  subject:
    topic: Mathematics
  subject:
    topic: Operator Theory
  subject:
    topic: Analysis
  subject:
    topic: Functional Analysis
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  subject:
    topic: Integral Equations
  subject:
    topic: Numerical Analysis
  classification: QA329-329.9
  classification: 515.724
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 1965
  identifier: 9781848821903
  identifier: http://dx.doi.org/10.1007/978-1-84882-190-3
  record info:
    record creation date: 100301
    record change date: 20151204175513.0
    record identifier: 978-1-84882-190-3