Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 560248, 15 pages
http://dx.doi.org/10.1155/2012/560248
Research Article

System of Nonlinear Set-Valued Variational Inclusions Involving a Finite Family of 𝐻(,)-Accretive Operators in Banach Spaces

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 15 February 2012; Accepted 27 March 2012

Academic Editor: Giuseppe Marino

Copyright © 2012 Prapairat Junlouchai and Somyot Plubtieng. 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. A. Hassouni and A. Moudafi, “A perturbed algorithm for variational inclusions,” Journal of Mathematical Analysis and Applications, vol. 185, no. 3, pp. 706–712, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. S. Adly, “Perturbed algorithms and sensitivity analysis for a general class of variational inclusions,” Journal of Mathematical Analysis and Applications, vol. 201, no. 2, pp. 609–630, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. X. P. Ding, “Perturbed proximal point algorithms for generalized quasivariational inclusions,” Journal of Mathematical Analysis and Applications, vol. 210, no. 1, pp. 88–101, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. K. R. Kazmi, “Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions,” Journal of Mathematical Analysis and Applications, vol. 209, no. 2, pp. 572–584, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. 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
  6. Q. H. Ansari, S. Schaible, and J. C. Yao, “System of vector equilibrium problems and its applications,” Journal of Optimization Theory and Applications, vol. 107, no. 3, pp. 547–557, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. Plubtieng and K. Sombut, “Weak convergence theorems for a system of mixed equilibrium problems and nonspreading mappings in a Hilbert space,” Journal of Inequalities and Applications, vol. 2010, Article ID 246237, 12 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Plubtieng and K. Sitthithakerngkiet, “On the existence result for system of generalized strong vector quasiequilibrium problems,” Fixed Point Theory and Applications, vol. 2011, Article ID 475121, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. Plubtieng and T. Thammathiwat, “Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems in G-convex spaces,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 124–130, 2011. View at Publisher · View at Google Scholar
  10. R. U. Verma, “A-monotonicity and applications to nonlinear variational inclusion problems,” Journal of Applied Mathematics and Stochastic Analysis, no. 2, pp. 193–195, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. 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
  12. S. Plubtieng and W. Sriprad, “A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 567147, 20 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. U. Verma, “General nonlinear variational inclusion problems involving A-monotone mappings,” Applied Mathematics Letters, vol. 19, no. 9, pp. 960–963, 2006. View at Publisher · View at Google Scholar
  14. Y. J. Cho, H.-Y. Lan, and R. U. Verma, “Nonlinear relaxed cocoercive variational inclusions involving (A,η)-accretive mappings in Banach spaces,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1529–1538, 2006. View at Publisher · View at Google Scholar
  15. 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
  16. Y.-Z. Zou and N.-J. Huang, “H(·,·)-accretive operator with an application for solving variational inclusions in Banach spaces,” Applied Mathematics and Computation, vol. 204, no. 2, pp. 809–816, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. Y. Z. Zou and N. J. Huang, “A new system of variational inclusions involving H(·, ·)-accretive operator in Banach spaces,” Applied Mathematics and Computation, vol. 212, pp. 135–144, 2009. View at Google Scholar
  18. H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. 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
  20. S. B. Nadler,, “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Google Scholar · View at Zentralblatt MATH