Geometric Properties of Banach Spaces and Nonlinear Iterations

• Main Author: Chidume, Charles. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London, 2009.
• Series: Lecture Notes in Mathematics, 1965
• Subjects: Mathematics.; Functional analysis.; Integral equations.; Operator theory.; Numerical analysis.; Mathematical optimization.; Operator Theory.; Calculus of Variations and Optimal Control; Optimization.; Functional Analysis.; Integral Equations.; Numerical Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-84882-190-3

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...

Table of 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 Points of 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
• 18. Finite Families of Lipschitz Pseudo-contractive and Accretive Mappings
• 19. Generalized Lipschitz Pseudo-contractive and Accretive Mappings
• 20. Finite Families of Non-self Asymptotically Nonexpansive Mappings
• 21. Families of Total Asymptotically Nonexpansive Maps
• 22. Common Fixed Points for One-parameter Nonexpansive Semigroup
• 23. Single-valued Accretive Operators; Applications; Some Open Questions
• References
• Index.