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General Strongly Nonlinear Quasivariational Inequalities with Relaxed Lipschitz and Relaxed Monotone Mappings

Author

Listed:
  • Z. Liu

    (Liaoning Normal University)

  • J.S. Ume

    (Changwon National University)

  • S.M. Kang

    (Gyeongsang National University)

Abstract

In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others.

Suggested Citation

  • Z. Liu & J.S. Ume & S.M. Kang, 2002. "General Strongly Nonlinear Quasivariational Inequalities with Relaxed Lipschitz and Relaxed Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 639-656, September.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:3:d:10.1023_a:1016079130417
    DOI: 10.1023/A:1016079130417
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