A general iterative method with strongly positive operators for general variational inequalities
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- 作者：Lu-Chuan Ceng ; Sy-Ming Guu ; Jen-Chih Yao
- 关键词：General iterative method ; Viscosity approximation ; Fixed point ; Inverse-strongly monotone mapping ; Nonexpansive mapping ; General variational inequality ; Strongly positive operator
- 刊名：Computers and Mathematics with Applications
- 出版年：2010
- 出版时间：February 2010
- 年：2010
- 卷：59
- 期：4
- 页码：1441-1452
- 全文大小：788 K
文摘
In this paper, we introduce and study a general iterative method with strongly positive operators for finding solutions of a general variational inequality problem with inverse-strongly monotone mapping in a real Hilbert space. The explicit and implicit iterative algorithms are proposed by virtue of the general iterative method with strongly positive operators. Under two sets of quite mild conditions, we prove the strong convergence of these explicit and implicit iterative algorithms to the unique common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality problem, respectively.