Applied Mathematics and Mechanics (English Edition) ›› 1994, Vol. 15 ›› Issue (4): 307-315.

• Articles • Previous Articles     Next Articles

GENERALIZED STRONGLY NONLINEAR QUASI-COMPLEMENTARITY PROBLEMS

Li Hong-mei, Ding Xie-ping   

  1. Sichuan Normal University, Chengdu
  • Received:1992-10-17 Online:1994-04-18 Published:1994-04-18
  • Supported by:

    Project supported by the National Natural Science Foundation of China

Abstract: Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.

Key words: maximal element, family of G B-majorized mappings, coincidence theorem, minimax inequalities, product space of G-convex space, generalized strongly nonlinear quasi-complementarity problem, Hilbert space, cone, H-Lipschitz continuous mapping with re-spect to g, ψ-strongly monotone mapping with respect to g

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