A general iterative method for hierarchical variational inequality problems in Hilbert spaces and applications

Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H . Let F be a maximal monotone operator on H such that the domain of F is included in C . Let 0...

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Veröffentlicht in:Positivity Jg. 16; H. 3; S. 429 - 453
Hauptverfasser: Lin, Lai-Jiu, Takahashi, Wataru
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel Springer Science and Business Media LLC 01.09.2012
SP Birkhäuser Verlag Basel
Springer
Springer Nature B.V
Schlagworte:
Calculus of variations and optimal control
Calculus of Variations and Optimal Control; Optimization
Econometrics
Equilibrium
Exact sciences and technology
Fourier Analysis
Hilbert space
Inequality
Iterative methods
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Operator Theory
Partial differential equations
Potential Theory
Sciences and techniques of general use
Studies
Variance analysis
Asia
58E35
47H10
Resolvent
Equilibrium problem
Inverse-strongly monotone mapping
Strict pseudo-contraction
Maximal monotone operator
Iteration procedure
47H05
Fixed point
Hierarchical variational inequality problems
Space application
Solution uniqueness
Strong convergence
Variational methods
Nonlinear analysis
Iterative method
Mapping
Monotone operator
Contraction
Mathematical analysis
Variational inequality
Hilbert problem
Hilbert space
Inverse
ISSN:1385-1292, 1572-9281
Online-Zugang:Volltext
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Zusammenfassung:Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H . Let F be a maximal monotone operator on H such that the domain of F is included in C . Let 0 < k  < 1 and let g be a k -contraction of H into itself. Let V be a -strongly monotone and L -Lipschitzian continuous operator with and L > 0. Take as follows: In this paper, under the assumption , we prove a strong convergence theorem for finding a point which is a unique solution of the hierarchical variational inequality Using this result, we obtain new and well-known strong convergence theorems in a Hilbert space which are useful in nonlinear analysis and optimization.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-012-0161-0