scholarly journals An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

2011 ◽  
Vol 92 ◽  
pp. 177-196
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Approximation Method ◽  
Equilibrium Problems ◽  
Infinite Family ◽  
Variational Inclusion ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Contractive Mappings ◽  
Mixed Equilibrium Problems

scholarly journals Iterative Algorithms for Mixed Equilibrium Problems, System of Quasi-Variational Inclusion, and Fixed Point Problem in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Poom Kumam ◽  
Thanyarat Jitpeera
Keyword(s):  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Variational Inclusion ◽  
Common Element ◽  
Point Problem ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for approximating a common element of the set of solutions for mixed equilibrium problems, the set of solutions of a system of quasi-variational inclusion, and the set of fixed points of an infinite family of nonexpansive mappings in a real Hilbert space. Strong convergence of the proposed iterative algorithm is obtained. Our results generalize, extend, and improve the results of Peng and Yao, 2009, Qin et al. 2010 and many authors.

scholarly journals Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Tanom Chamnarnpan ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
Common Element ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

scholarly journals A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Uamporn Witthayarat ◽  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Steepest Descent ◽  
Common Element ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Weakly Contractive Mapping ◽  
Minimization Problems ◽  
Weakly Contractive

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.

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.

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