Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces

DOI10.1081/NFA-120023869zbMath1071.47052OpenAlexW2050149585MaRDI QIDQ4435186

Zaslavski, Alexander J., Dan Butnariu, Simeon Reich

Publication date: 26 November 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-120023869

zbMATH Keywords

weak convergencefixed pointreflexive Banach spaceorbituniform convexityBergman distancetotal convexitynonexpansiveness with respect to a convex function

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Baire category, Baire spaces (54E52) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical methods for mathematical programming, optimization and variational techniques (65K99)

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Cites Work

• Unnamed Item
• Averaged mappings in the Hilbert ball
• Generic flows generated by continuous vector fields in Banach spaces
• Some generic properties in fixed point theory
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• An iterative row-action method for interval convex programming
• Geometry of Banach spaces. Selected topics
• Iterative averaging of entropic projections for solving stochastic convex feasibility problems
• Iterative methods of solving stochastic convex feasibility problems and applications
• Generic power convergence of order-preserving mappings
• Totally convex functions for fixed points computation and infinite dimensional optimization
• Infinite products of resolvents of accretive operators
• Existence of solutions of optimal control problems for a generic integrand without convexity assumptions
• Weak convergence theorems for asymptotically nonexpansive mappings and semigroups
• Generic Convergence of Descent Methods in Banach Spaces
• A limit theorem for projections
• Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces
• Convergence of generic infinite products of nonexpansive and uniformly continuous operators
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
• Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
• Generic power convergence of operators in banach spaces
• Dynamic properties of optimal solutions of variational problems
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
• Best approximation in inner product spaces

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