• Published : 2004.02.01


In this paper, we suggest and analyze some new classes of three step iterative algorithms for solving generalized quasivariational inclusions by using the properties of proximal maps. Our results include the Ishikawa, Mann iterations for solving variational inclusions(inequalities) as special cases. The results obtained in this paper represent an improvement and significant refinement of previously known results [3, 5-8, 10, 14-18].


variational inclusions;resolvent equations;algorithms;iterative methods


  1. J. Math. Anal. Appl. v.210 Perturbed proximal point algorithms for generalized quasivariational inclusions
  2. J. Math. Anal. Appl. v.251 New approximation schemes for general variational inequalities
  3. J. Math. Anal. Appl. v.209 Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions K.R.Kazmi
  4. Indian J. Pure Appl. Math. v.25 On nonlinear variational inequalities A.H.Siddiqu;Q.H.Ansari;K.R.Kazmi
  5. J. Math. Anal. Appl. v.166 General strongly nonlinear variational inequalities
  6. J. Math. Anal. Appl. v.201 Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities
  7. SIAM Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics R.Glowinski;P. Le Tallee
  8. J. Math. Anal. Appl. v.158 An iterative algorithm for variational inequalities
  9. Appl. Math. Lett. v.14 A predictor corrector algorithm for general variational inequalities
  10. Appl. Math. Lett v.1 General variational inequalities M.A.Noor
  11. J. Math. Anal. Appl. v.173 Generalized strongly nonlinear quasivariational inequalities X.P.Ding
  12. J. Global Optim. v.19 Iterative schemes for multivalued quasivariational inequalities
  13. Math. Japon v.34 An iterative method for generalized variational inequalities A.H.Siddiqu;Q.H.Ansari
  14. J. Natur. Geom. v.14 Resolvent equations and variational inclusions
  15. J. Math. Anal. Appl. v.187 Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities L.C.Zeng
  16. New Zealand J. Math v.26 Some recent advances in variational inequalities, Part II, Other concepts
  17. Indian J. Pure Appl. Math. v.25 A new class of generalized strongly nonlinear quasivariational inequalities and quasicomplementarity problems
  18. J. Math. Anal. Appl. v.185 A perturbed algorithm for variational inclusions A.Hassouni;A.Moudafi