Modified hybrid iterative methods for generalized mixed equilibrium, variational inequality and fixed point problems

被引:2
作者
Jung, Jong Soo [1 ]
机构
[1] Dong A Univ, Dept Math, Busan 49315, South Korea
来源
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 07期
关键词
Hybrid iterative method; generalized mixed equilibrium problem; continuous monotone mapping; continuous pseudocontractive mapping; variational inequality; fixed point; rho-Lipschitzian and eta-strongly monotone mapping; metric projection; STRONG-CONVERGENCE THEOREMS; NONEXPANSIVE-MAPPINGS; WEAK-CONVERGENCE; ALGORITHM; SCHEME;
D O I
10.22436/jnsa.010.07.30
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we introduce two modified hybrid iterative methods (one implicit method and one explicit method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality problem for a continuous monotone mapping and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces, and show under suitable control conditions that the sequences generated by the proposed iterative methods converge strongly to a common element of three sets, which solves a certain variational inequality. As a direct consequence, we obtain the unique minimum-norm common point of three sets. The results in this paper substantially improve upon, develop and complement the previous well-known results in this area. (C) 2017 All rights reserved.
引用
收藏
页码:3732 / 3754
页数:23
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