Abstract and Applied Analysis

Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

Zhao-Rong Kong, Lu-Chuan Ceng, Qamrul Hasan Ansari, and Chin-Tzong Pang

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Abstract

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 718624, 17 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393442741

Digital Object Identifier
doi:10.1155/2013/718624

Mathematical Reviews number (MathSciNet)
MR3045059

Zentralblatt MATH identifier
1272.49062

Citation

Kong, Zhao-Rong; Ceng, Lu-Chuan; Ansari, Qamrul Hasan; Pang, Chin-Tzong. Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 718624, 17 pages. doi:10.1155/2013/718624. https://projecteuclid.org/euclid.aaa/1393442741


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