TY - JOUR
A2 - Yao, Jen-Chih
AU - Kong, Zhao-Rong
AU - Ceng, Lu-Chuan
AU - Ansari, Qamrul Hasan
AU - Pang, Chin-Tzong
PY - 2013
DA - 2013/04/17
TI - Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities
SP - 718624
VL - 2013
AB - 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.
SN - 1085-3375
UR - https://doi.org/10.1155/2013/718624
DO - 10.1155/2013/718624
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -