Strong convergence results of two-steps modifying Halpern's iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application

DOI10.1186/1029-242X-2014-412zbMath1337.47091OpenAlexW2139328190WikidataQ59324576 ScholiaQ59324576MaRDI QIDQ257806

Yi Li, Hong Bo Liu

Publication date: 17 March 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2014-412

zbMATH Keywords

fixed pointLegendre functionsBregman projectionBregman strongly nonexpansive multi-valued mappingtwo-steps modifying Halpern's iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Set-valued operators (47H04) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Halpern-Mann's iterations for Bregman strongly nonexpansive mappings in reflexive Banach spaces with applications
• Right Bregman nonexpansive operators in Banach spaces
• Strong convergence theorems for Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces
• Convex functions, monotone operators and differentiability.
• Halpern's iteration for Bregman strongly nonexpansive mappings in reflexive Banach spaces
• Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces
• The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces
• The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces
• An iterative row-action method for interval convex programming
• An iterative approach to quadratic optimization
• Totally convex functions for fixed points computation and infinite dimensional optimization
• Bregman strongly nonexpansive operators in reflexive Banach spaces
• Iterative methods for approximating fixed points of Bregman nonexpansive operators
• Halpern's iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application
• Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
• 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
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Fixed points of nonexpanding maps
• Gradients of Convex Functions
• Convex Analysis