关键词: 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

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