An implicit iterative scheme for monotone variational inequalities and fixed point problems

被引：21

作者：

Ceng, L. C. ^{[3
]}

Cubiotti, R. ^{[2
]}

Yaoc, J. C. ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] Univ Messina, Dept Math, I-98166 Messina, Italy

[3] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 08期

关键词：

variational inequality; nonexpansive mapping; implicit iterative scheme; monotone mapping; fixed point; weak convergence; demiclosedness principle; opial's condition;

D O I：

10.1016/j.na.2007.08.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce an implicit iterative scheme for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The implicit iterative scheme is based on two well-known methods: extragradient and approximate proximal. We obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme. On the basis of this theorem, we also construct an implicit iterative process for finding a common fixed point of N + 1 mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other N mappings are nonexpansive. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：2445 / 2457

页数：13

共 50 条

[1] An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems
Alansari, Monairah
Farid, Mohammad
Ali, Rehan
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[2] An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems
Monairah Alansari
Mohammad Farid
Rehan Ali
[J]. Advances in Difference Equations, 2020
[3] Correction to: An iterative scheme for split monotone variational inclusion, variational inequality, and fixed point problems
Monairah Alansari
Mohammad Farid
Rehan Ali
[J]. Advances in Continuous and Discrete Models, 2023
[4] Iterative algorithms for solving fixed point problems and variational inequalities with uniformly continuous monotone operators
Shehu, Yekini
Iyiola, Olaniyi S.
[J]. NUMERICAL ALGORITHMS, 2018, 79 (02) : 529 - 553
[5] Iterative algorithms for solving fixed point problems and variational inequalities with uniformly continuous monotone operators
Yekini Shehu
Olaniyi S. Iyiola
[J]. Numerical Algorithms, 2018, 79 : 529 - 553
[6] Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems
Liou, Yeong-Cheng
Yao, Yonghong
Tseng, Chun-Wei
Lin, Hui-To
Yang, Pei-Xia
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[7] Monotone variational inequalities, generalized equilibrium problems and fixed point methods
Shenghua Wang
[J]. Fixed Point Theory and Applications, 2014
[8] Monotone variational inequalities, generalized equilibrium problems and fixed point methods
Wang, Shenghua
[J]. FIXED POINT THEORY AND APPLICATIONS, 2014,
[9] An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems
Sitthithakerngkiet, Kanokwan
Deepho, Jitsupa
Martinez-Moreno, Juan
Kumam, Poom
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (12) : 2373 - 2395
[10] An iterative scheme for split monotone variational inclusion, variational inequality, and fixed point problems (vol 2020, 485, 2020)
Alansari, Monairah
Farid, Mohammad
Ali, Rehan
[J]. ADVANCES IN CONTINUOUS AND DISCRETE MODELS, 2023, 2023 (01):

← 1 2 3 4 5 →