Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THREE STEP ITERATIVE ALGORITHMS FOR GENERALIZED QUASIVARIATIONAL INCLUSIONS

  • Published : 2004.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

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].

Keywords

References

  1. J. Math. Anal. Appl. v.173 Generalized strongly nonlinear quasivariational inequalities X.P.Ding https://doi.org/10.1006/jmaa.1993.1089
  2. Indian J. Pure Appl. Math. v.25 A new class of generalized strongly nonlinear quasivariational inequalities and quasicomplementarity problems
  3. J. Math. Anal. Appl. v.210 Perturbed proximal point algorithms for generalized quasivariational inclusions https://doi.org/10.1006/jmaa.1997.5370
  4. SIAM Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics R.Glowinski;P. Le Tallee
  5. J. Math. Anal. Appl. v.185 A perturbed algorithm for variational inclusions A.Hassouni;A.Moudafi https://doi.org/10.1006/jmaa.1994.1277
  6. J. Math. Anal. Appl. v.209 Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions K.R.Kazmi https://doi.org/10.1006/jmaa.1997.5368
  7. Appl. Math. Lett v.1 General variational inequalities M.A.Noor https://doi.org/10.1016/0893-9659(88)90054-7
  8. J. Math. Anal. Appl. v.158 An iterative algorithm for variational inequalities https://doi.org/10.1016/0022-247X(91)90248-X
  9. New Zealand J. Math v.26 Some recent advances in variational inequalities, Part II, Other concepts
  10. J. Natur. Geom. v.14 Resolvent equations and variational inclusions
  11. J. Math. Anal. Appl. v.251 New approximation schemes for general variational inequalities https://doi.org/10.1006/jmaa.2000.7042
  12. Appl. Math. Lett. v.14 A predictor corrector algorithm for general variational inequalities https://doi.org/10.1016/S0893-9659(00)00112-9
  13. J. Global Optim. v.19 Iterative schemes for multivalued quasivariational inequalities https://doi.org/10.1023/A:1008320428781
  14. Math. Japon v.34 An iterative method for generalized variational inequalities A.H.Siddiqu;Q.H.Ansari
  15. J. Math. Anal. Appl. v.166 General strongly nonlinear variational inequalities https://doi.org/10.1016/0022-247X(92)90305-W
  16. Indian J. Pure Appl. Math. v.25 On nonlinear variational inequalities A.H.Siddiqu;Q.H.Ansari;K.R.Kazmi
  17. J. Math. Anal. Appl. v.187 Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities L.C.Zeng https://doi.org/10.1006/jmaa.1994.1361
  18. J. Math. Anal. Appl. v.201 Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities https://doi.org/10.1006/jmaa.1996.0249