scholarly journals Modified Noor's Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Shunhou Fan ◽  
Shin Min Kang ◽  
Muhammad Aslam Noor ◽  
Yonghong Yao
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Extragradient Method ◽  
Sunny Nonexpansive Retraction ◽  
Extragradient Methods ◽  
Generalized Variational Inequalities

Motivated and inspired by Korpelevich's and Noor's extragradient methods, we suggest an extragradient method by using the sunny nonexpansive retraction which has strong convergence for solving the generalized variational inequalities in Banach spaces.

scholarly journals Extended Extragradient Methods for Generalized Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Cun-Lin Li ◽  
Hui-To Lin
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Extragradient Methods ◽  
Generalized Variational Inequalities ◽  
Mild Conditions ◽  
Convergence Results ◽  
Special Cases

We suggest a modified extragradient method for solving the generalized variational inequalities in a Banach space. We prove some strong convergence results under some mild conditions on parameters. Some special cases are also discussed.

Modified inertial subgradient extragradient method for equilibrium problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Yekini Shehu ◽  
Regina N. Nwokoye
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Weak And Strong Convergence ◽  
Extragradient Methods ◽  
Convergence Results ◽  
Inertial Extrapolation ◽  
Special Case

Abstract The subgradient extragradient method with inertial extrapolation step x n + θ n (x n − x n−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.

scholarly journals Mann-Type Extragradient Methods for General Systems of Variational Inequalities with Multivalued Variational Inclusion Constraints in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Lu-Chuan Ceng ◽  
Abdul Latif ◽  
Saleh A. Al-Mezel
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
General System ◽  
Variational Inclusion ◽  
Uniformly Convex ◽  
Extragradient Methods ◽  
Extragradient Algorithm

We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich’s extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces

2009 ◽  
Vol 110 (3) ◽  
pp. 1211-1224 ◽  
Author(s):  
Yonghong Yao ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Yeong-Cheng Liou ◽  
Huma Yaqoob
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Extragradient Methods ◽  
System Of Variational Inequalities
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