Taiwanese Journal of Mathematics

AN ITERATIVE METHOD FOR GENERALIZED MIXED VECTOR EQUILIBRIUM PROBLEMS AND FIXED POINT OF NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITIES

Shu-qiang Shan and Nan-jing Huang

Full-text: Open access

Abstract

In this paper, we study the problem of finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the generalized mixed vector equilibrium problem and the solution set of a variational inequality problem with a monotone Lipschitz continuous mapping in Hilbert spaces. We first consider an auxiliary problem for the generalized mixed vector equilibrium problem and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the generalized mixed vector equilibrium problem and the solution set of a variational inequality problem with a monotone Lipschitz continuous mapping. The results presented in this paper can be considered as a generalization of some known results due to Peng and Yao [16, 17].

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1681-1705.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406790

Digital Object Identifier
doi:10.11650/twjm/1500406790

Mathematical Reviews number (MathSciNet)
MR2970678

Zentralblatt MATH identifier
1252.49012

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Keywords
generalized mixed vector equilibrium problem auxiliary problem variational inequality nonexpansive mapping iterative scheme

Citation

Shan, Shu-qiang; Huang, Nan-jing. AN ITERATIVE METHOD FOR GENERALIZED MIXED VECTOR EQUILIBRIUM PROBLEMS AND FIXED POINT OF NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITIES. Taiwanese J. Math. 16 (2012), no. 5, 1681--1705. doi:10.11650/twjm/1500406790. https://projecteuclid.org/euclid.twjm/1500406790


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