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

被引：22

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
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
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
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.
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
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
ABSTRACT AND APPLIED ANALYSIS, 2012,
[7] Monotone variational inequalities, generalized equilibrium problems and fixed point methods
Shenghua Wang
Fixed Point Theory and Applications, 2014
[8] Monotone variational inequalities, generalized equilibrium problems and fixed point methods
Wang, Shenghua
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
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
ADVANCES IN CONTINUOUS AND DISCRETE MODELS, 2023, 2023 (01):

← 1 2 3 4 5 →