Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving (A, η)-Maximal Relaxed Monotone Operators

We introduce and study a class of new general systems of set-valued variational inclusions involving (A,η)-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with (A,η)-maximal relaxed monotone operators, we construct some new iterative...

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2014; no. 2014; pp. 670 - 677-662
Main Authors Xiong, Ting-jian, Lan, Heng-you
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Algorithms
Approximation
Artificial intelligence
Colleges & universities
Construction
Control systems
Convergence
Cybernetics
Estimates
Inclusions
Iterative algorithms
Iterative methods (Mathematics)
Mathematical analysis
Mathematical models
Mathematical research
Monotonic functions
Operators
Science
Variational principles
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Summary:We introduce and study a class of new general systems of set-valued variational inclusions involving (A,η)-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with (A,η)-maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2014/698593