Outer Approximation Method for Constrained Composite Fixed Point Problems Involving Lipschitz Pseudo Contractive Operators

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these operators and an outer approximation given by the projection on...

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Vydáno v:Numerical functional analysis and optimization Ročník 32; číslo 11; s. 1099 - 1115
Hlavní autor: Briceño-Arias, Luis M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Taylor & Francis Group 01.11.2011
Taylor & Francis
Témata:
Equilibrium problem
Exact sciences and technology
Firmly nonexpansive operator
Fixed point problems
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Monotone inclusion
Monotone operator
Primary 65K05
Pseudo contractive operator
Sciences and techniques of general use
Secondary 47H05
Splitting algorithm
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Monotone inclusion
Approximation
Pseudo contractive operator
Iteration
Monotone operator
Algorithm
Convergence
Splitting
Fix point
Equilibrium problem
Problem solving
Splitting algorithm
Hilbert space
Fixed point problems
Firmly nonexpansive operator
ISSN:0163-0563, 1532-2467
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Popis
Shrnutí:We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these operators and an outer approximation given by the projection onto a closed half-space containing the constraint set. Its convergence is established and applications to monotone inclusion splitting and constrained equilibrium problems are demonstrated.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2011.594199