Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

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Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2013-257 ◽

2013 ◽

Vol 2013 (1) ◽

Author(s):

Ci-Shui Ge ◽

Neng-Fu Yu ◽

Lin Zhao

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Strong Convergence ◽

Equilibrium Problems ◽

Iterative Algorithms ◽

Variable Coefficients ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

Generalized Equilibrium

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A General Iterative Method for Variational Inequality Problems, Mixed Equilibrium Problems, and Fixed Point Problems of Strictly Pseudocontractive Mappings in Hilbert Spaces

Fixed Point Theory and Applications ◽

10.1155/2009/519065 ◽

2009 ◽

Vol 2009 (1) ◽

pp. 519065 ◽

Cited By ~ 5

Author(s):

Rattanaporn Wangkeeree ◽

Rabian Wangkeeree

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Iterative Method ◽

Hilbert Spaces ◽

Equilibrium Problems ◽

Variational Inequality Problems ◽

Pseudocontractive Mappings ◽

Mixed Equilibrium Problems ◽

General Iterative Method ◽

Strictly Pseudocontractive Mappings

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Strong convergence theorems for nonlinear mappings, variational inequality problems and system of generalized mixed equilibrium problems

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2011.05.035 ◽

2011 ◽

Vol 54 (9-10) ◽

pp. 2259-2276 ◽

Cited By ~ 4

Author(s):

Yekini Shehu

Keyword(s):

Variational Inequality ◽

Strong Convergence ◽

Equilibrium Problems ◽

Variational Inequality Problems ◽

Convergence Theorems ◽

Generalized Mixed Equilibrium Problems ◽

Mixed Equilibrium Problems ◽

Generalized Mixed Equilibrium ◽

Mixed Equilibrium ◽

Nonlinear Mappings

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Strong convergence theorem by a new hybrid method for equilibrium problems and variational inequality problems

Nonlinear Analysis ◽

10.1016/j.na.2009.07.037 ◽

2010 ◽

Vol 72 (2) ◽

pp. 847-855 ◽

Cited By ~ 13

Author(s):

Li HongYu ◽

Su YongFu

Keyword(s):

Variational Inequality ◽

Strong Convergence ◽

Hybrid Method ◽

Convergence Theorem ◽

Equilibrium Problems ◽

Variational Inequality Problems ◽

Strong Convergence Theorem

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Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2007.12.008 ◽

2008 ◽

Vol 48 (7-8) ◽

pp. 1033-1046 ◽

Cited By ~ 81

Author(s):

Xiaolong Qin ◽

Meijuan Shang ◽

Yongfu Su

Keyword(s):

Variational Inequality ◽

Strong Convergence ◽

Iterative Algorithm ◽

Equilibrium Problems ◽

Variational Inequality Problems

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A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

Journal of Inequalities and Applications ◽

10.1186/1029-242x-2011-51 ◽

2011 ◽

Vol 2011 (1) ◽

Cited By ~ 1

Author(s):

Jong Soo Jung

Keyword(s):

Variational Inequality ◽

Iterative Method ◽

Equilibrium Problems ◽

Optimization Problems ◽

Variational Inequality Problems ◽

Generalized Mixed Equilibrium Problems ◽

Mixed Equilibrium Problems ◽

Generalized Mixed Equilibrium ◽

Mixed Equilibrium

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CONVERGENCE ANALYSIS ON HYBRID PROJECTION ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2009.14.335-351 ◽

2009 ◽

Vol 14 (3) ◽

pp. 335-351 ◽

Cited By ~ 12

Author(s):

Xiaolong Qin ◽

Yeol Je Cho ◽

Shin Min Kang

Keyword(s):

Banach Space ◽

Fixed Point ◽

Variational Inequality ◽

Iterative Method ◽

Convergence Analysis ◽

Equilibrium Problems ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

Projection Algorithms

In this paper, we consider an iterative method for equilibrium problems, fixed point problems and variational inequality problems in the framework of Banach space. The results presented in this paper improve and extend the corresponding results announced by many others.

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