Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 698593, 8 pages
http://dx.doi.org/10.1155/2014/698593
Research Article

Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving -Maximal Relaxed Monotone Operators

1Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, China
2Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, Sichuan 643000, China

Received 24 March 2014; Accepted 16 May 2014; Published 5 June 2014

Academic Editor: Jian-Wen Peng

Copyright © 2014 Ting-jian Xiong and Heng-you Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y.-P. Fang, N.-J. Huang, and H.-B. Thompson, “A new system of variational inclusions with (H,η)-monotone operators in Hilbert spaces,” Computers & Mathematics with Applications, vol. 49, no. 2-3, pp. 365–374, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  2. W.-Y. Yan, Y.-P. Fang, and N.-J. Huang, “A new system of set-valued variational inclusions with H-monotone operators,” Mathematical Inequalities & Applications, vol. 8, no. 3, pp. 537–546, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Y.-P. Fang and N.-J. Huang, “H-monotone operators and system of variational inclusions,” Communications on Applied Nonlinear Analysis, vol. 11, no. 1, pp. 93–101, 2004. View at Google Scholar · View at MathSciNet
  4. H.-W. Cao, “Sensitivity analysis for a system of generalized nonlinear mixed quasi variational inclusions with H-monotone operators,” Journal of Applied Mathematics, vol. 2011, Article ID 921835, 15 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H.-Y. Lan, J.-H. Kim, and Y.-J. Cho, “On a new system of nonlinear A-monotone multivalued variational inclusions,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 481–493, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. H.-Y. Lan, “A class of nonlinear (A,η)-monotone operator inclusion problems with relaxed cocoercive mappings,” Advances in Nonlinear Variational Inequalities, vol. 9, no. 2, pp. 1–11, 2006. View at Google Scholar · View at MathSciNet
  7. J.-W. Peng and L.-J. Zhao, “General system of A-monotone nonlinear variational inclusions problems with applications,” Journal of Inequalities and Applications, vol. 2009, Article ID 364615, 13 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. R.-U. Verma, “A-monotonicity and applications to nonlinear variational inclusion problems,” Journal of Applied Mathematics and Stochastic Analysis, vol. 17, no. 2, pp. 193–195, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R.-P. Agarwal and R.-U. Verma, “General system of (A,η)-maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 238–251, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R.-U. Verma, “Sensitivity analysis for generalized strongly monotone variational inclusions based on the (A,η)-resolvent operator technique,” Applied Mathematics Letters, vol. 19, no. 12, pp. 1409–1413, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  11. X.-P. Ding and C.-L. Luo, “Perturbed proximal point algorithms for general quasi-variational-like inclusions,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 153–165, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y.-P. Fang and N.-J. Huang, “H-monotone operator and resolvent operator technique for variational inclusions,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 795–803, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. N.-J. Huang and Y.-P. Fang, “A new class of general variational inclusions involving maximal η-monotone mappings,” Publicationes Mathematicae Debrecen, vol. 62, no. 1-2, pp. 83–98, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M.-M. Jin, “Generalized nonlinear implicit quasivariational inclusions with relaxed monotone mappings,” Advances in Nonlinear Variational Inequalities, vol. 7, no. 2, pp. 173–181, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M.-M. Jin, “Iterative algorithm for a new system of nonlinear set-valued variational inclusions involving (H,η)-monotone mappings,” Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, article 72, 10 pages, 2006. View at Google Scholar · View at MathSciNet
  16. R.-P. Agarwal, N.-J. Huang, and Y.-J. Cho, “Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings,” Journal of Inequalities and Applications, vol. 7, no. 6, pp. 807–828, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R.-U. Verma, “Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings,” Journal of Mathematical Analysis and Applications, vol. 337, no. 2, pp. 969–975, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. N.-J. Huang and Y.-P. Fang, “Fixed point theorems and a new system of multivalued generalized order complementarity problems,” Positivity, vol. 7, no. 3, pp. 257–265, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R.-U. Verma, “Projection methods, algorithms, and a new system of nonlinear variational inequalities,” Computers & Mathematics with Applications, vol. 41, no. 7-8, pp. 1025–1031, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y.-J. Cho, Y.-P. Fang, N.-J. Huang, and H.-J. Hwang, “Algorithms for systems of nonlinear variational inequalities,” Journal of the Korean Mathematical Society, vol. 41, no. 3, pp. 489–499, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J.-K. Kim and D.-S. Kim, “A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces,” Journal of Convex Analysis, vol. 11, no. 1, pp. 235–243, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. R.-U. Verma, “Generalized system for relaxed cocoercive variational inequalities and projection methods,” Journal of Optimization Theory and Applications, vol. 121, no. 1, pp. 203–210, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. G. Kassay and J. Kolumbán, “System of multi-valued variational inequalities,” Publicationes Mathematicae Debrecen, vol. 56, no. 1-2, pp. 185–195, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y. Yao, Y.-C. Liou, C.-L. Li, and H.-T. Lin, “Extended extragradient methods for generalized variational inequalities,” Journal of Applied Mathematics, vol. 2012, Article ID 237083, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M.-A. Noor, K.-I. Noor, Z. Huang, and E. Al-Said, “Implicit schemes for solving extended general nonconvex variational inequalities,” Journal of Applied Mathematics, vol. 2012, Article ID 646259, 10 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. S.-B. Nadler Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, no. 2, pp. 475–488, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet