scholarly journals Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
P. Cholamjiak ◽  
W. Cholamjiak ◽  
S. Suantai
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Equilibrium Problems ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Viscosity Approximation Methods

AbstractIn this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

scholarly journals Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds

2015 ◽  
Vol 4 (2) ◽  
pp. 299
Author(s):  
Mandeep Kumari ◽  
Renu Chugh
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Approximation Method ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Hadamard Manifolds ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>

scholarly journals Viscosity Approximation Methods for a Family of Nonexpansive Mappings in CAT(0) Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jinfang Tang
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Problem ◽  
Iterative Schemes ◽  
The Family ◽  
Viscosity Approximation Methods ◽  
Implicit And Explicit

The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

scholarly journals Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Aihong Wang
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Pseudocontractive Mappings ◽  
Viscosity Approximation Methods

We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of the solutions of the equilibrium problem and the set of fixed points of infinitely strict pseudocontractive mappings. Strong convergence theorems are established in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently.

scholarly journals Strong Convergence Results for Equilibrium Problems and Fixed Point Problems for Multivalued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Vahidi ◽  
A. Latif ◽  
M. Eslamian
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Finite Family ◽  
Common Element ◽  
Multivalued Mappings ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Results

Using viscosity approximation method, we study strong convergence to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued mappings satisfying the condition (E) in the setting of Hilbert space. Our results improve and extend some recent results in the literature.

scholarly journals Convergence Theorems of Variational Inequality for Asymptotically Nonexpansive Nonself Mapping in CAT(0) Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1234
Author(s):  
Kyung Soo Kim
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Viscosity Approximation Methods

The aim of this manuscript is to get the strong convergence theorems of the Moudafi’s viscosity approximation methods for an asymptotically nonexpansive nonself mapping in C A T ( 0 ) spaces.

scholarly journals Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Luo Yi Shi ◽  
Ru Dong Chen
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Convex Subset ◽  
Unique Fixed Point ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mappingTof a closed convex subsetCof a CAT(0) spaceX. Suppose that the set Fix(T)of fixed points ofTis nonempty. For a contractionfonCandt∈(0,1), letxt∈Cbe the unique fixed point of the contractionx↦tf(x)⊕(1-t)Tx. We will show that ifXis a CAT(0) space satisfying some property, then{xt}converge strongly to a fixed point ofTwhich solves some variational inequality. Consider also the iteration process{xn}, wherex0∈Cis arbitrary andxn+1=αnf(xn)⊕(1-αn)Txnforn≥1, where{αn}⊂(0,1). It is shown that under certain appropriate conditions onαn,{xn}converge strongly to a fixed point ofTwhich solves some variational inequality.

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