Strong convergence of a modified iterative algorithm for hierarchical fixed point problems and variational inequalities

This article aims to deal with a new modified iterative projection method for solving a hierarchical fixed point problem. It is shown that under certain approximate assumptions of the operators and parameters, the modified iterative sequence { x n } converges strongly to a fixed point x ∗ of T , als...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2013; no. 1
Main Authors: Wang, Yuanheng, Xu, Wei
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.05.2013
Subjects:
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Recent Trends on Fixed Point Theory and its Applications
Topology
hierarchical fixed point
nonexpansive mapping
modified iterative projection algorithm
quadratic minimization
Lipschitzian and strongly monotone mapping
ISSN:1687-1812, 1687-1812
Online Access:Get full text
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Summary:This article aims to deal with a new modified iterative projection method for solving a hierarchical fixed point problem. It is shown that under certain approximate assumptions of the operators and parameters, the modified iterative sequence { x n } converges strongly to a fixed point x ∗ of T , also the solution of a variational inequality. As a special case, this projection method solves some quadratic minimization problem. The results here improve and extend some recent corresponding results by other authors. MSC: 47H10, 47J20, 47H09, 47H05.
ISSN:1687-1812
1687-1812
DOI:10.1186/1687-1812-2013-121