Iterative algorithms for hierarchical fixed points problems and variational inequalities

This paper deals with a method for approximating a solution of the fixed point problem: find x ̃ ∈ H ; x ̃ = ( proj F ( T ) ⋅ S ) x ̃ , where H is a Hilbert space, S is some nonlinear operator and T is a nonexpansive mapping on a closed convex subset C and proj F ( T ) denotes the metric projection...

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Bibliographic Details
Published in:Mathematical and computer modelling 2010-11, Vol.52 (9), p.1697-1705
Main Authors: Yao, Yonghong, Cho, Yeol Je, Liou, Yeong-Cheng
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Hierarchical fixed point problems
Iterative algorithms
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonexpansive mappings
Numerical analysis. Scientific computation
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Variational inequalities
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Summary:This paper deals with a method for approximating a solution of the fixed point problem: find x ̃ ∈ H ; x ̃ = ( proj F ( T ) ⋅ S ) x ̃ , where H is a Hilbert space, S is some nonlinear operator and T is a nonexpansive mapping on a closed convex subset C and proj F ( T ) denotes the metric projection on the set of fixed points of T . First, we prove a strong convergence theorem by using a projection method which solves some variational inequality. As a special case, this projection method also solves some minimization problems. Secondly, under different restrictions on parameters, we obtain another strong convergence result which solves the above fixed point problem.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.06.038