Sensitivity Analysis for Generalized Nonlinear Implicit Quasi-variational Inclusions

  • Received : 2005.02.01
  • Published : 2006.09.23

Abstract

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a new class of parametric generalized nonlinear implicit quasi-variational inclusion problem in $L_p(p{\geq}2)$ spaces. The results presented in this paper are new and generalize many known results in this field.

Keywords

References

  1. S. Adly, Perturbed algorithms and sensitivity analysis for a general class of variational inclusions, J. Math. Anal. Appl., 201(1996), 609-630. https://doi.org/10.1006/jmaa.1996.0277
  2. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Internat. Publ. Leyden, The Netherlands, 1976.
  3. C. E. Chidume, Iterative solution of nonlinear equations of the monotone and dissipative type, Appl. Anal., 33(1989), 79-86. https://doi.org/10.1080/00036818908839862
  4. C. E. Chidume, An iterative process for nonlinear Lipschitzian strongly accretive mappings in $L_{p}$ spaces, J. Math. Anal. Appl., 151(2)(1990), 453-461. https://doi.org/10.1016/0022-247X(90)90160-H
  5. S. Dafermos, Sensitivity analysis in variational inequalities, Mathematics of Operators Research, 13(1988), 421-434. https://doi.org/10.1287/moor.13.3.421
  6. X. P. Ding, Perturbed proximal point algorithm for generalized quasivariational inclusions, J. Math. Anal. Appl., 210(1997), 88-101. https://doi.org/10.1006/jmaa.1997.5370
  7. X. P. Ding and C. L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory and Appl., 100(1)(1999), 195-205. https://doi.org/10.1023/A:1021777217261
  8. A. Hassouni and A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl., 185(1994), 706-721. https://doi.org/10.1006/jmaa.1994.1277
  9. N. J. Huang, Mann and Ishikawa type perturbed iterative algorithms for nonlinear implicit quasivariational inclusions, Computers Math. Appl., 35(10)(1998), 9-14.
  10. K. R. Kazmi, Mann and Ishikawa perturbed iterative algorithms for generalized quasivariational inclusions, J. Math. Anal. Appl., 35(10)(1998), 9-14.
  11. Shu Jie Li and De Xing Feng, The topological degree for multivalued maximal monotone operator in Hilbert spaces, Acta Math. Sinica, 25(5)(1982), 533-541.
  12. T. C. Lim, On fixed point stability for set-valued contractive mappings with application to generalized differential equations, J. Math. Anal. Appl., 110(1985), 436-441. https://doi.org/10.1016/0022-247X(85)90306-3
  13. R. N. Mukherjee and H. L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl., 167(1992), 299-304. https://doi.org/10.1016/0022-247X(92)90207-T
  14. S. B. Nadler, Multi-valued contraction mappings, Pacafic J. Math., 30(1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  15. M. A. Noor, General algorithm and sensitivity analysis for variational inequalities, Journal of Applied Mathematics and Stochastic Analysis, 5(1992), 29-42. https://doi.org/10.1155/S1048953392000030
  16. M. A. Noor, Generalized set-valued variational inclusions and resolvent equations, J. Math. Anal. Appl., 228(1998), 206-220. https://doi.org/10.1006/jmaa.1998.6127
  17. M. A. Noor, K. I. Noor and T. M. Rassias, Set-valued resolvent equations and mixed variational inequalities, J. Math. Anal. Appl., 220(1998), 741-759. https://doi.org/10.1006/jmaa.1997.5893
  18. Y. H. Pan, Sensitivity analysis for general quasi-variational inequalities, Journal of the Sichuan Normal University, 19(1996), 56-59.
  19. J. Y. Park and J. U. Jeong, Parametric generalized mixed variational inequalities, Applied Mathematics and Letters, 17(2004), 43-48. https://doi.org/10.1016/S0893-9659(04)90009-2
  20. N. D. Yen, Lipschitz continuity of solution of variational inequalities with a parametric polyhedral constraint, Mathematics of Operations Research, 20(1995), 695-708. https://doi.org/10.1287/moor.20.3.695