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Fixed-Point Technique for Implicit Complementarity Problem in Hilbert Lattice

Author

Listed:
  • K. Ahmad

    (Jamia Millia Islamia)

  • K. R. Kazmi

    (Jamia Millia Islamia)

  • N. Rehman

    (Jamia Millia Islamia)

Abstract

In this paper, we consider and study the implicit complementarity problem in the setting of a Hilbert lattice. It has been shown that this problem can be formulated as a fixed-point problem by using a suitable change of variables. Moreover, this formulation allows us to prove the existence and uniqueness of solutions of the implicit complementarity problem.

Suggested Citation

  • K. Ahmad & K. R. Kazmi & N. Rehman, 1997. "Fixed-Point Technique for Implicit Complementarity Problem in Hilbert Lattice," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 67-72, April.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:1:d:10.1023_a:1022645716916
    DOI: 10.1023/A:1022645716916
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. M. A. Noor & E. A. Al-Said, 1999. "Change of Variable Method for Generalized Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 389-395, February.

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