Abstract
In this paper,. by using the auxiliary technique of variational inequalities, the existence and iterative algorithms of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results answer the open problems mentioned by Noor, improve and generalize some recent known results.
Similar content being viewed by others
References
Noor M A. General algorithm for variational inequalities[J].Math Japonica, 1993,38 (1): 47–53.
Noor M A, Noor K I. Iterative methods for variational inequalities[J].Methods Oper Res, 1979,31: 455–463.
Noor M A. An iterative scheme for a class of quasi-variational inequalities[J].J Math Anal Appl, 1985,110: 463–468.
Noor M A. General nonlinear variational inequalities[J].J Math Anal Appl, 1987,126: 78–84.
Glowinski R, Lions J L, Tremolieres R.Numerical Analysis of Variational Inequatities [M]. Amsterdam: North-Holland, 1981.
Noor M A. Mixed variational inequalities[J].Appl Math Lett, 1990,3(2): 73–75.
Noor M A. An iterative algorithm for nonlinear variational inequalities[J].Appl Math Lett, 1992,5(4): 11–14.
Cohen G. Auxiliary problem extended to variational inequalities[J].J Optim Theor Appl, 1988,59: 325–333.
Siddiqi A H, Ansari Q H. Strongly nonlinear quasi-variational inequalities[J].J Math Anal Appl, 1990,149: 444–450.
Ding Xieping. Generalized strongly nonlinear quasi-variational inequalities[J].J Math Anal Appl, 1993,173(2): 577–587.
Zhang Shisheng. Fixed Point Theory With Applications[M]. Chongqing: Chongqing Press, 1984 (in Chinese)
Zhang Shisheng,Variational Inequalities and Complementarity Problem Theory With Applications [M]. Shanghai: Shanghai Science Technical Document Press, 1991. (in Chinese)
Nadler S B, Jr. Multi-valued contraction mapping[J],Pacific J Math, 1969,30:475–488.
Author information
Authors and Affiliations
Additional information
Communicated by Ding Xieping
Foundation item: the Natural Science Foundation of Sichuan Education Committee (1988-142)
Rights and permissions
About this article
Cite this article
Chunlin, L. Existence and iterative algorithms of solutions for generalized mixed quasi-variational inequalities. Appl Math Mech 20, 1038–1045 (1999). https://doi.org/10.1007/BF02459068
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02459068
Key words
- generalized mixed quasi-variational inequalities
- strongly monotone
- Lipschutz continuous
- Hausdorff metric