Advertisement

Applied Mathematics and Mechanics

, Volume 15, Issue 11, pp 1069–1080 | Cite as

Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities

  • Zeng Lu-chuan
Article

Abstract

In this paper, we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include. as a special case, some known results in this field. Our results are the extension and improvements of the results of Siddiqi and Ansari, Ding, and Zeng.

Key words

quasivariational inequality iterative scheme convergence of algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Boyd, D. W. and Wong J. S. W., On nonlinear contractions,Proc. Amer. Math. Soc., 20 (1969), 458–464.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Browder, F. E., The fixed point theory of multivalued mappings in topological vector spaces.Math. Ann. 177 (1968) 283–301.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Ding, X. P., Iterative methods of solutions for generalized variational inequalities and complementarity problems.J. Sichuan Normal Univ.,14 (1991), 1–5.Google Scholar
  4. [4]
    Fang, S. C. and E. L. Peterson. Generalized variational inequalities.J. Optim. Theory Appl. 38 (1982), 363–383.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Zeng Lu-chuan. Completely generalized strongly nonlinear quasivariational inequalities.J. Math. Anal. Appl. submitted for publication.Google Scholar
  6. [6]
    Kinderlehrar D. and G. Stampacchia,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, (1980).Google Scholar
  7. [7]
    Noor, M. A., Strongly nonlinear variational inequalities.C. R. Math. Rep. Acad. Sci., Canada,4 (1982), 213–218.zbMATHMathSciNetGoogle Scholar
  8. [8]
    Noor, M. A., An iterative scheme for a class of quasivariational inequalities.J. Math. Anal. Appl.,111 (1985), 463–468.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Noor, M. A., On the nonlinear complementarity problem.J. Math. Anal. Appl.,123, (1987), 455–460.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Noor, M. A., Quasivariational inequalities,Appl. Math. Lett. 1 (1988), 367–370.zbMATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    Rockafellar, R. T., Lagrange multipliers and variational inequalities, in “Variational Inequalities and Complementarity Problems. Theory and Applications” (Cottle et al., Eds.), New York (1980), 303–322.Google Scholar
  12. [12]
    Saigal, R., Extension of the generalized complementarity problem,Math. Oper. Res., 1 (1976), 260–266.zbMATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    Siddiqi, A. H. and Q. H. Ansari, An interative method for generalized variational inequalities.Math. Japan.,34 (1989), 475–481.zbMATHMathSciNetGoogle Scholar
  14. [14]
    Siddiqi, A. H. and Q. H. Ansari, Strongly nonlinear quasivariational inequalities,J. Math. Anal. Appl.,149 (1990), 444–450.zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    Siddiqi, A. H. and Q. H. Ansari, General strongly nonlinear variational inequalities.J. Math. Anal. Appl.,166 (1992), 386–392.zbMATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    Zeng Lu-chuan, Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities,J. Math. Appl..Google Scholar
  17. [17]
    Ding, X. P., Generalized strongly nonlinear quasivariational inequalities,J. Math. Anal Appl.,173 (1993), 577–587.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Zeng Lu-chuan
    • 1
  1. 1.Department of MathematicsShanghai Normal UniversityShanghai

Personalised recommendations