Right Bregman nonexpansive operators in Banach spaces
From MaRDI portal
Publication:450585
DOI10.1016/j.na.2012.04.048zbMath1408.47011OpenAlexW1994761593MaRDI QIDQ450585
Victoria Martín-Márquez, Shoham Sabach, Simeon Reich
Publication date: 13 September 2012
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://idus.us.es/xmlui/handle/11441/47199
resolventreflexive Banach spaceretractionBregman distanceLegendre functionmonotone mappingtotally convex functionnonexpansive operator\(T\)-monotone mappingBoltzmann-Shannon entropyBregman firmly nonexpansive operatorFermi-Dirac entropy
Set-valued operators (47H04) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)
Related Items
A common solution of f-fixed point and variational inequality problems in Banach spaces ⋮ Iterative solution of split variational inclusion problem in a real Banach spaces ⋮ Convergence theorems for maximal monotone operators and fixed point problems in Banach spaces ⋮ Strong convergence of hybrid Halpern iteration for Bregman totally quasi-asymptotically nonexpansive multi-valued mappings in reflexive Banach spaces with application ⋮ Strong convergence theorem for quasi-Bregman strictly pseudocontractive mappings and equilibrium problems in Banach spaces ⋮ An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces ⋮ Revisiting jointly firmly nonexpansive families of mappings ⋮ Unnamed Item ⋮ An inertial method for split equality common \(f, g\)-fixed point problems of \(f, g\)-pseudocontractive mappings in reflexive real Banach spaces ⋮ An inertial self-adaptive iterative algorithm for finding the common solutions to split feasibility and fixed point problems in specific Banach spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A common solution of split equality monotone inclusion problem and split equality fixed point problem in real Banach spaces ⋮ Unnamed Item ⋮ Convergence theorems for right Bregman strongly nonexpansive mappings in reflexive Banach spaces ⋮ A modified iterative algorithm for split feasibility problems of right Bregman strongly quasi-nonexpansive mappings in Banach spaces with applications ⋮ Approximation of a common \(f\)-fixed point of \(f\)-pseudocontractive mappings in Banach spaces ⋮ Solving the split feasibility problem and the fixed point problem of left Bregman firmly nonexpansive mappings via the dynamical step sizes in Banach spaces ⋮ Existence of common fixed points using Bregman nonexpansive retracts and Bregman functions in Banach spaces ⋮ Halpern's iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application ⋮ Unnamed Item ⋮ Existence and Approximation of Fixed Points of Right Bregman Nonexpansive Operators ⋮ The modified Ishikawa iterative algorithm with errors for a countable family of Bregman totally quasi-\(D\)-asymptotically nonexpansive mappings in reflexive Banach spaces ⋮ Strong convergence theorem for split feasibility problems and variational inclusion problems in real Banach spaces ⋮ Solutions to inexact resolvent inclusion problems with applications to nonlinear analysis and optimization ⋮ Convergence analysis of an iterative algorithm for fixed point problems and split feasibility problems in certain Banach spaces ⋮ Approximation of common solutions for system of equilibrium problems and fixed-point problems ⋮ Convergence theorems for equilibrium and fixed point problems ⋮ On split equality for finite family of generalized mixed equilibrum problem and fixed point problem in real Banach spaces ⋮ Convergence analysis of an iterative method for solving multiple-set split feasibility problems in certain Banach spaces ⋮ Compositions and convex combinations of Bregman weakly relatively nonexpansive operators in reflexive Banach spaces ⋮ Strong convergence of a system of generalized mixed equilibrium problem, split variational inclusion problem and fixed point problem in Banach spaces ⋮ Strong convergence of Halpern iteration for products of finitely many resolvents of maximal monotone operators in Banach spaces ⋮ Strong convergence results of two-steps modifying Halpern's iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application ⋮ On split equality equilibrium, monotone variational inclusion and fixed point problems in Banach spaces
Cites Work
- Convex functions, monotone operators and differentiability.
- Convex analysis and nonlinear optimization. Theory and examples.
- Bregman distances and Chebyshev sets
- An iterative row-action method for interval convex programming
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- Extension problems for accretive sets in Banach spaces
- Iterative averaging of entropic projections for solving stochastic convex feasibility problems
- Totally convex functions for fixed points computation and infinite dimensional optimization
- Nonexpansive projections on subsets of Banach spaces
- Asymptotic behavior of contractions in Banach spaces
- Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
- Chebyshev Sets, Klee Sets, and Chebyshev Centers with Respect to Bregman Distances: Recent Results and Open Problems
- Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces
- Bregman Monotone Optimization Algorithms
- ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
- Fixed points of quasi-nonexpansive mappings
- Convex analysis and monotone operator theory in Hilbert spaces
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item