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

被引：11

作者：

Yao, Yonghong ^{[1
]}

Liou, Yeong-Cheng ^{[2
]}

Chen, Rudong ^{[1
]}

机构：

[1] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

[2] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan

来源：

MATHEMATISCHE NACHRICHTEN | 2009年 / 282卷 / 12期

关键词：

Fixed point; monotone mapping; variational inequality; strong convergence; Hilbert space; NONEXPANSIVE-MAPPINGS; MONOTONE-OPERATORS;

D O I：

10.1002/mana.200610817

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an alpha-inverse strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under some mild conditions on parameters. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1827 / 1835

页数：9

共 50 条

[21] CONVERGENCE THEOREMS OF COMMON SOLUTIONS FOR FIXED POINT, VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS
Shahzad, Naseer
Zegeye, Habtu
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2019, 3 (02): : 189 - 203
[22] Synchronal algorithm and cyclic algorithm for fixed point problems and variational inequality problems in hilbert spaces
Ming Tian
Lanyun Di
Fixed Point Theory and Applications, 2011
[23] Synchronal algorithm and cyclic algorithm for fixed point problems and variational inequality problems in hilbert spaces
Tian, Ming
Di, Lanyun
FIXED POINT THEORY AND APPLICATIONS, 2011,
[24] NEW CONVERGENCE THEOREMS FOR SPLIT COMMON FIXED POINT PROBLEMS IN HILBERT SPACES
Shehu, Yekini
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2015, 16 (01) : 167 - 181
[25] Strong convergence theorems for variational inequalities and fixed point problems in Banach spaces
Nnakwe, M. O.
Ezeora, J. N.
CARPATHIAN JOURNAL OF MATHEMATICS, 2021, 37 (03) : 477 - 487
[26] STRONG CONVERGENCE THEOREMS FOR GENERAL VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN q-UNIFORMLY SMOOTH BANACH SPACES
Cai, Gang
Bu, Shangquan
FIXED POINT THEORY, 2012, 13 (02): : 383 - 401
[27] Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces
Cai, Gang
Bu, Shangquan
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (06) : 2567 - 2579
[28] Strong convergence theorems for fixed point problems, variational inequality problems and system of generalized mixed equilibrium problems
Shehu, Yekini
MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (5-6) : 1510 - 1522
[29] A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces
Wangkeeree, Rabian
Preechasilp, Pakkapon
JOURNAL OF APPLIED MATHEMATICS, 2012,
[30] Strong and Weak Convergence Theorems for General Mixed Equilibrium, General Variational Inequality, and Fixed Point Problems for Two Nonexpansive Semigroups in Hilbert Spaces
Zhang, Baoshuai
Tian, Ying
RUSSIAN PHYSICS JOURNAL, 2021, 64 (05) : 937 - 948

← 1 2 3 4 5 →