About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 643828, 21 pages
http://dx.doi.org/10.1155/2012/643828
Research Article

On a System of Nonlinear Variational Inclusions with -Monotone Operators

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea
3Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 15 August 2012; Accepted 11 October 2012

Academic Editor: Yongfu Su

Copyright © 2012 Zeqing Liu et al. 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. R. Ahmad and Q. H. Ansari, “Generalized variational inclusions and H-resolvent equations with H-accretive operators,” Taiwanese Journal of Mathematics, vol. 11, no. 3, pp. 703–716, 2007.
  2. Q. H. Ansari and J.-C. Yao, “A fixed point theorem and its applications to a system of variational inequalities,” Bulletin of the Australian Mathematical Society, vol. 59, no. 3, pp. 433–442, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. T. Cai, Z. Liu, and S. M. Kang, “Existence of solutions for a system of generalized nonlinear implicit variational inequalities,” Mathematical Sciences Research Journal, vol. 8, no. 6, pp. 176–183, 2004. View at Zentralblatt MATH
  4. T. Cai, Z. Liu, S. H. Shim, and S. M. Kang, “Approximation-solvability of a system of generalized nonlinear mixed variational inequalities,” Advances in Nonlinear Variational Inequalities, vol. 8, no. 1, pp. 63–70, 2005. View at Zentralblatt MATH
  5. 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
  6. 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 Zentralblatt MATH
  7. G. Kassay, J. Kolumbán, and Z. Páles, “Factorization of Minty and Stampacchia variational inequality systems,” European Journal of Operational Research, vol. 143, no. 2, pp. 377–389, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. 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.
  9. H.-Y. Lan, Y.-S. Cui, and Y. Fu, “New approximation-solvability of general nonlinear operator inclusion couples involving (A,η,m)-resolvent operators and relaxed cocoercive type operators,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1844–1851, 2012. View at Publisher · View at Google Scholar
  10. H.-Y. Lan, Y. Li, and J. Tang, “Existence and iterative approximations of solutions for nonlinear implicit fuzzy resolvent operator systems of (A,η)-monotone type,” Journal of Computational Analysis and Applications, vol. 13, no. 2, pp. 335–344, 2011.
  11. Z. Liu, Y. Hao, S. K. Lee, and S. M. Kang, “On a system of general quasivariational-like inequalities,” Mathematical Sciences Research Journal, vol. 9, no. 4, pp. 92–100, 2005. View at Zentralblatt MATH
  12. Z. Liu, Y. Hao, S. M. Kang, and W. Chung, “On a system of generalized nonlinear variational inequalities,” Panamerican Mathematical Journal, vol. 15, no. 1, pp. 95–106, 2005. View at Zentralblatt MATH
  13. H. Nie, Z. Liu, K. H. Kim, and S. M. Kang, “A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings,” Advances in Nonlinear Variational Inequalities, vol. 6, no. 2, pp. 91–99, 2003. View at Zentralblatt MATH
  14. R. U. Verma, “Computational role of partially relaxed monotone mappings in solvability of a system of nonlinear variational inequalities,” Advances in Nonlinear Variational Inequalities, vol. 3, no. 2, pp. 79–86, 2000. View at Zentralblatt MATH
  15. 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
  16. R. U. Verma, “Approximation-solvability of a two-step system of relaxed g-γ-r-cocoercive nonlinear variational inequalities based on projection methods,” Advances in Nonlinear Variational Inequalities, vol. 7, no. 1, pp. 87–94, 2004.
  17. 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
  18. B. E. Rhoades and R. U. Verma, “Two-step algorithms and their applications to variational problems,” Communications on Applied Nonlinear Analysis, vol. 11, no. 2, pp. 45–55, 2004. View at Zentralblatt MATH
  19. Q. H. Wu, Z. Liu, S. H. Shim, and S. M. Kang, “Approximation-solvability of a new system of nonlinear variational inequalities,” Mathematical Sciences Research Journal, vol. 7, no. 8, pp. 338–346, 2003. View at Zentralblatt MATH
  20. L. S. Liu, “Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 114–125, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH