A new completely general class of variational inclusions with noncompact valued mappings

Computers and Mathematics with Applications

Volumn 35, Issue 10, 1998, Pages 9-14

  Huang, Nan Jing ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Algorithm; Convergence; Existence; Set valued mapping; Variational inclusion

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; MATHEMATICAL TECHNIQUES;

SET VALUED MAPPING; VARIATIONAL INCLUSIONS;

VARIATIONAL TECHNIQUES;

EID: 0032066154     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00067-4     Document Type: Article

References (26)

1. P. Hartman and G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta. Math. 115, 271-310, (1966).
2. A. Bensoussan, M. Goursat and J.L. Lions, Control impulsinnel et inequations quasivariationalles stationaries, C. R. Acad. Sci. 276, 1279-1284, (1973).
3. C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities, Application to Free Boundary Problems, Wiley, New York, (1984).
4. A. Bensoussan, Stochastic Control by Functional Analysis Method, North-Holland, Amsterdam, (1982).
5. A. Bensoussan and J.L. Lions, Impulse Control and Quasivariational Inequalities, Gauthiers-Villers, Bordas, Paris, (1984).
6. S. Chang, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Scientific and Tech. Literature Publishing House, Shanghai, (1991).
7. G. Isac, Complementarity problems, In Lecture Notes in Mathematics, Springer-Verlag, Heidelberg, (1992).
8. U. Mosco, Implicit variational problems and quasi-variational inequalities, In Lecture Notes in Mathematics, Volume 543, pp. 83-156, Springer-Verlag, Berlin, (1976).
9. S. Chang and N. Huang, Generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces, J. Math. Anal. Appl. 158, 194-202, (1991).
10. S. Chang and N. Huang, Generalized multivalued implicit complementarity problems in Hilbert spaces, Math. Japonica 36, 1093-1100, (1991).
11. S. Adly, Perturbed algorithm and sensitivity analysis for a general class of variational inclusions, J. Math. Anal. Appl. 201, 609-630, (1996).
12. M.A. Noor, Strongly nonlinear variational inequalities, C. R. Math. Rep. Acad. Sci. Canada 4, 213-218, (1982).
13. M.A. Noor, On the nonlinear complementarity problem, J. Math. Anal Appl. 123, 455-460, (1987).
14. M.A. Noor, Quasivariational inequalities, Appl. Math. Lett. 1 (4), 367-370, (1988).
15. G. Isac, A special variational inequality and the implicit complementarity problem, J. Fac. Sci. Univ. Tokyo 37, 109-127, (1990).
16. A.H. Siddiqi and Q.H. Ansari, Strongly nonlinear quasivariational inequalities, J. Math. Anal. Appl. 149, 444-150, (1990).
17. A.H. Siddiqi and Q.H. Ansari, General strongly nonlinear variational inequalities, J. Math. Anal. Appl. 166, 386-392, (1992).
18. A. Hassouni and A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185, 706-712, (1994).
19. N. Huang, Generalized nonlinear variational inclusions with noncompact valued mapping, Appl. Math. Lett. 9 (3), 25-29, (1996).
20. S. Chang and N. Huang, Generalized quasi-complementarity problems for a pair of fuzzy mappings, J. Fuzzy Math. 4, 343-354, (1996).
21. X.P. Ding, Generalized strongly nonlinear quasivariational inequalities, J. Math. Anal. Appl. 173, 577-587, (1993).
22. N. Huang, Completely Generalized strongly nonlinear quasi-complementarity problems for fuzzy mappings, Indian J. Pure Appl. Math. 28, 23-32, (1997).
23. N. Huang, Completely generalized nonlinear variational inclusions for fuzzy mappings, Czech. Math. J. (to appear).
24. L. Zheng, Completely generalized strongly nonlinear quasicomplementarity problems in Hilbert spaces, J. Math. Anal. Appl. 193, 706-714, (1995).
25. L. Zheng, Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities, J. Math. Anal. Appl. 201, 180-194, (1996).
26. S.B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30, 475-488, (1969).