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.
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References
Boyd, D. W. and Wong J. S. W., On nonlinear contractions,Proc. Amer. Math. Soc., 20 (1969), 458–464.
Browder, F. E., The fixed point theory of multivalued mappings in topological vector spaces.Math. Ann. 177 (1968) 283–301.
Ding, X. P., Iterative methods of solutions for generalized variational inequalities and complementarity problems.J. Sichuan Normal Univ.,14 (1991), 1–5.
Fang, S. C. and E. L. Peterson. Generalized variational inequalities.J. Optim. Theory Appl. 38 (1982), 363–383.
Zeng Lu-chuan. Completely generalized strongly nonlinear quasivariational inequalities.J. Math. Anal. Appl. submitted for publication.
Kinderlehrar D. and G. Stampacchia,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, (1980).
Noor, M. A., Strongly nonlinear variational inequalities.C. R. Math. Rep. Acad. Sci., Canada,4 (1982), 213–218.
Noor, M. A., An iterative scheme for a class of quasivariational inequalities.J. Math. Anal. Appl.,111 (1985), 463–468.
Noor, M. A., On the nonlinear complementarity problem.J. Math. Anal. Appl.,123, (1987), 455–460.
Noor, M. A., Quasivariational inequalities,Appl. Math. Lett. 1 (1988), 367–370.
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.
Saigal, R., Extension of the generalized complementarity problem,Math. Oper. Res., 1 (1976), 260–266.
Siddiqi, A. H. and Q. H. Ansari, An interative method for generalized variational inequalities.Math. Japan.,34 (1989), 475–481.
Siddiqi, A. H. and Q. H. Ansari, Strongly nonlinear quasivariational inequalities,J. Math. Anal. Appl.,149 (1990), 444–450.
Siddiqi, A. H. and Q. H. Ansari, General strongly nonlinear variational inequalities.J. Math. Anal. Appl.,166 (1992), 386–392.
Zeng Lu-chuan, Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities,J. Math. Appl..
Ding, X. P., Generalized strongly nonlinear quasivariational inequalities,J. Math. Anal Appl.,173 (1993), 577–587.
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Lu-chuan, Z. Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities. Appl Math Mech 15, 1069–1080 (1994). https://doi.org/10.1007/BF02455398
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DOI: https://doi.org/10.1007/BF02455398