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

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  • Ting-jian Xiong
  • Heng-you Lan

Abstract

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.

Suggested Citation

  • Ting-jian Xiong & Heng-you Lan, 2014. "Iterative Algorithms for New General Systems of Set‐Valued Variational Inclusions Involving (A, η)‐Maximal Relaxed Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:698593
    DOI: 10.1155/2014/698593
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    References listed on IDEAS

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    1. Ram U. Verma, 2004. "A -monotonicity and applications to nonlinear variational inclusion problems," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-3, January.
    2. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, November.
    5. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, January.
    6. Han-Wen Cao, 2011. "Sensitivity Analysis for a System of Generalized Nonlinear Mixed Quasi Variational Inclusions with H -Monotone Operators," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-15, August.
    7. Han-Wen Cao, 2011. "Sensitivity Analysis for a System of Generalized Nonlinear Mixed Quasi Variational Inclusions with H‐Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
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