Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.11.004 ◽

2008 ◽

Vol 200 (1) ◽

pp. 242-253 ◽

Author(s):

Xiaolong Qin ◽

Meijuan Shang ◽

Haiyun Zhou

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Iterative Method ◽

Strong Convergence ◽

Hilbert Spaces ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

General Iterative Method

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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 ◽

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 of a new general iterative method for variational inequality problems in Hilbert spaces

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2012-46 ◽

2012 ◽

Vol 2012 (1) ◽

pp. 46 ◽

Author(s):

Yan-Lai Song ◽

Hui-Ying Hu ◽

Ya-Qin Wang ◽

Lu-Chuan Zeng ◽

Chang-Song Hu

Keyword(s):

Variational Inequality ◽

Iterative Method ◽

Strong Convergence ◽

Hilbert Spaces ◽

Variational Inequality Problems ◽

General Iterative Method

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A general iterative method for solving equilibrium problems, variational inequality problems and fixed point problems of an infinite family of nonexpansive mappings

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-009-0330-x ◽

2009 ◽

Vol 34 (1-2) ◽

pp. 407-439 ◽

Author(s):

Chaichana Jaiboon ◽

Poom Kumam

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Iterative Method ◽

Equilibrium Problems ◽

Nonexpansive Mappings ◽

Infinite Family ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

General Iterative Method

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A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces

Fixed Point Theory and Applications ◽

10.1155/2009/369215 ◽

2009 ◽

Vol 2009 (1) ◽

pp. 369215 ◽

Author(s):

Rabian Wangkeeree ◽

Uthai Kamraksa

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Iterative Method ◽

Hilbert Spaces ◽

Variational Inequality Problem ◽

Nonexpansive Mappings ◽

Infinite Family ◽

Fixed Point Problem ◽

Point Problem ◽

General Iterative Method

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STRONG CONVERGENCE THEOREM BY AN EXTRAGRADIENT METHOD FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

Taiwanese Journal of Mathematics ◽

10.11650/twjm/1500557303 ◽

2006 ◽

Vol 10 (5) ◽

pp. 1293-1303 ◽

Author(s):

Lu-Chuan Zeng ◽

Jen-Chih Yao

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Strong Convergence ◽

Convergence Theorem ◽

Extragradient Method ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

Strong Convergence Theorem

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Convergence theorems for fixed point problems and variational inequality problems in Hilbert spaces

Mathematische Nachrichten ◽

10.1002/mana.200610817 ◽

2009 ◽

Vol 282 (12) ◽

pp. 1827-1835 ◽

Author(s):

Yonghong Yao ◽

Yeong-Cheng Liou ◽

Rudong Chen

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Hilbert Spaces ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

Convergence Theorems

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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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Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces

Journal of Global Optimization ◽

10.1007/s10898-012-9923-2 ◽

2012 ◽

Vol 56 (4) ◽

pp. 1529-1542 ◽

Author(s):

Gang Cai ◽

Shangquan Bu

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Strong Convergence ◽

Banach Spaces ◽

Variational Inequality Problems ◽

Fixed Point Problems ◽

Uniformly Convex ◽

Convergence Theorems ◽

Uniformly Smooth ◽

Uniformly Convex Banach Spaces

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The modified viscosity implicit rules for variational inequality problems and fixed point problems of nonexpansive mappings in Hilbert spaces

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-019-00716-2 ◽

2019 ◽

Vol 113 (4) ◽

pp. 3545-3562 ◽

Author(s):

Gang Cai ◽

Yekini Shehu ◽

Olaniyi Samuel Iyiola

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Hilbert Spaces ◽

Nonexpansive Mappings ◽

Variational Inequality Problems ◽

Fixed Point Problems

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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 ◽

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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