Bregman weak relatively nonexpansive mappings in Banach spaces
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Publication:2250968
DOI10.1186/1687-1812-2013-141zbMath1423.47046OpenAlexW2167898805WikidataQ59300257 ScholiaQ59300257MaRDI QIDQ2250968
Jen-Chih Yao, Eskandar Naraghirad
Publication date: 22 July 2014
Published in: Fixed Point Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/1687-1812-2013-141
strong convergencefixed pointBregman functionuniformly convex functionuniformly smooth functionBregman weak relatively nonexpansive mapping
Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Modified block iterative algorithm for quasi-\(\phi\)-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces
- Strong convergence of modified iteration processes for relatively asymptotically nonexpansive mappings
- A strong convergence theorem for relatively nonexpansive mappings in a Banach space
- A projection method for solving nonlinear problems in reflexive Banach spaces
- Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type
- Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings
- Convergence of a modified Halpern-type iteration algorithm for quasi-\(\phi\)-nonexpansive mappings
- Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces
- Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces
- Fixed point iterations for nonlinear Hammerstein equation involving nonexpansive and accretive mappings
- Weak convergence theorems for nonexpansive mappings in Banach spaces
- An iterative row-action method for interval convex programming
- An example concerning fixed points
- Iterative averaging of entropic projections for solving stochastic convex feasibility problems
- On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
- Totally convex functions for fixed points computation and infinite dimensional optimization
- Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
- On hybrid projection methods for asymptotically quasi-\(\phi\)-nonexpansive mappings
- Strong convergence theorems for relatively nonexpansive mappings in a Banach space
- Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces
- Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
- Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space
- Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
- Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
- Characterization of the subdifferentials of convex functions
- On the maximal monotonicity of subdifferential mappings
- Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces
- Products of Finitely Many Resolvents of Maximal Monotone Mappings in Reflexive Banach Spaces
- Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods
- Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces
- A limit theorem for projections
- On the Convergence of the Proximal Point Algorithm for Convex Minimization
- Monotone Operators and the Proximal Point Algorithm
- Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
- Construction of best Bregman approximations 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
- Monotone operators and nonlinear integral equations of Hammerstein type
- Maximal monotone operators and nonlinear integral equations of Hammerstein type
- On the Maximality of Sums of Nonlinear Monotone Operators
- On the Variational Method for the Existence of Solutions of Nonlinear Equations of Hammerstein Type
- A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
- Mean Value Methods in Iteration