Split nonconvex variational inequality problem

被引：6
作者：
Kazmi K.R. [1 ]
机构：
[1] Department of Mathematics, Aligarh Muslim University, Aligarh
来源：
Mathematical Sciences | 2013年 / 7卷 / 1期
关键词：
Iterative methods; Split convex variational inequality problem; Split nonconvex variational inequality problem; Uniform prox-regularity;
D O I：
10.1186/2251-7456-7-36
中图分类号：
学科分类号：
摘要：
In this paper, we propose a split nonconvex variational inequality problem which is a natural extension of split convex variational inequality problem in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new split nonconvex variational inequality problem. Further, we also establish the convergence of an iterative method for the split convex variational inequality problem. The results presented in this paper are new and different form the previously known results for nonconvex (convex) variational inequality problems. These results also generalize, unify, and improve the previously known results of this area. 2010 MSC: Primary 47J53, 65K10; Secondary 49M37, 90C25 © 2013, Kazmi; licensee Springer.
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