Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 709715, 20 pages
http://dx.doi.org/10.5402/2011/709715
Research Article

( 𝐻 , 𝜙 ) - 𝜂 -Accretive Mappings and a New System of Generalized Variational Inclusions with ( 𝐻 , 𝜙 ) - 𝜂 -Accretive Mappings in Banach Spaces

Department of Mathematics, Yasouj University, Yasouj 75914, Iran

Received 5 June 2011; Accepted 29 June 2011

Academic Editors: Y.-K. Chang and Z. Hou

Copyright © 2011 Sayyedeh Zahra Nazemi. 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. P. Agarwal, Y. J. Cho, and N. J. Huang, “Sensitivity analysis for strongly nonlinear quasi-variational inclusions,” Applied Mathematics Letters, vol. 13, no. 6, pp. 19–24, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. 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
  3. R. Ahmad and Q. H. Ansari, “An iterative algorithm for generalized nonlinear variational inclusions,” Applied Mathematics Letters, vol. 13, no. 5, pp. 23–26, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S.-S. Chang, Y. J. Cho, and H. Y. Zho, “On the iterative approximation methods of fixed points for asymptotically contractive type mappings in Banach spaces,” in Fixed Point Theory and Applications. Vol. 3, pp. 33–41, Nova Science Publishers, Huntington, NY, USA, 2002. View at Google Scholar
  5. X. P. Ding, “Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities,” Applied Mathematics and Computation, vol. 113, no. 1, pp. 67–80, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. 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
  8. Y. P. Fang and N. J. Huang, “Approximate solutions for nonlinear operator inclusions with -(H,η)-monotone operators,” Tech. Rep., Sichuan University, 2003. View at Google Scholar
  9. Y.-P. Fang and N.-J. Huang, “H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces,” Applied Mathematics Letters, vol. 17, no. 6, pp. 647–653, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. N. J. Huang and Y. P. Fang, “Generalized m-accretive mappings in Banach spaces,” Journal of Sichuan University, vol. 38, no. 4, pp. 591–592, 2001. View at Google Scholar
  11. Y. P. Fang, Y. J. Cho, and J. K. Kim, “(H,η)-accretive operators and approximating solutions for systems of variational inclusions in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications. In press.
  12. K. R. Kazmi and F. A. Khan, “Iterative approximation of a solution of multi-valued variational-like inclusion in Banach spaces: a P-η-proximal-point mapping approach,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 665–674, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. H.-Y. Lan, “On multivalued nonlinear variational inclusion problems with (A,η)-accretive mappings in Banach spaces,” Journal of Inequalities and Applications, Article ID 59836, 12 pages, 2006. View at Google Scholar
  14. H.-Y. Lan, Y. J. Cho, 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 · View at MathSciNet
  15. X.-P. Luo and N.-J. Huang, “(H,η)-η-monotone operators in Banach spaces with an application to variational inclusions,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1131–1139, 2010. View at Publisher · View at Google Scholar
  16. 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 · View at MathSciNet
  17. Z. B. Xu and G. F. Roach, “Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 157, no. 1, pp. 189–210, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990.
  19. 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 · View at MathSciNet
  20. H.-Y. Lan, “Stability of iterative processes with errors for a system of nonlinear (A,η)-accretive variational inclusions in Banach spaces,” Computers & Mathematics with Applications, vol. 56, no. 1, pp. 290–303, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. E. Zeidler, Functional Analysis and its Applications II: Monotone Operators, Springer, New York, NY, USA, 1985.
  22. Y. J. Cho and X. Qin, “Systems of generalized nonlinear variational inequalities and its projection methods,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 12, pp. 4443–4451, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. 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
  24. G. Kassay and J. Kolumbán, “System of multi-valued variational inequalities,” Publicationes Mathematicae Debrecen, vol. 54, pp. 267–279, 1999. View at Google Scholar
  25. 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
  26. S. B. Nodler, “Multivalued contraction mapping,” Pacific Journal of Mathematics, vol. 30, no. 3, pp. 457–488, 1969. View at Google Scholar