General iterative methods for monotone mappings and pseudocontractive mappings related to optimization problems
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- 作者：Jong Soo Jung
- 关键词：general iterative method ; optimization problem ; continuous monotone mapping ; continuous pseudocontractive mapping ; variational inequality ; metric projection ; strongly positive bounded linear operator ; contractive mapping
- 刊名：Fixed Point Theory and Applications
- 出版年：2015
- 出版时间：December 2015
- 年：2015
- 卷：2015
- 期：1
- 全文大小：1,658 KB
- 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
- 出版者：Springer International Publishing
- ISSN：1687-1812
文摘
In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a continuous monotone mapping and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Under some control conditions, we establish the strong convergence of the proposed methods to a common element of the solution set and the fixed point set, which is the unique solution of a certain optimization problem. As a direct consequence, we obtain the unique minimum-norm common point of the solution set and the fixed point set.