Generalized multivalued quasi-variational inequalities

Computers and Mathematics with Applications

Volumn 31, Issue 12, 1996, Pages 1-13

  Noor, M A ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Convergence analysis; Fixed points; Iterative algorithms; Variational inequalties; Wiener Hopf equations

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; EQUIVALENCE CLASSES; ITERATIVE METHODS; NUMERICAL METHODS;

FIXED POINTS; GENERALIZED MULTIVALUED QUASI VARIATIONAL INEQUALITIES; ITERATIVE ALGORITHMS; PROJECTION TECHNIQUE; WIENER-HOPF EQUATIONS;

VARIATIONAL TECHNIQUES;

EID: 0030172722     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00071-5     Document Type: Article

References (48)

1. C. Baiocchi and A. Capelo, Variational and Quasi-Variational Inequalities, J. Wiley and Sons, New York, (1984).
2. A. Bensoussan and J.L. Lions, Applications des Inequations Variationelles en Control et en Stochastiques, Dunod, Paris, (1978).
3. D. Chan and J.S. Pang, The generalized quasi variational inequality problems, Math. Oper. Research 7, 211-222, (1982).
4. S.S. Chang and N.J. Huang, Generalized strongly nonlinear quasi complementarity problems in Hilbert space, J. Math. Anal. Appl. 158, 194-202, (1991).
5. R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem, Academic Press, New York, (1992).
6. R.W. Cottle, F. Giannessi and J.L. Lions, Variational Inequalities and Complementarity Problems: Theory and Applications, J. Wiley and Sons, New York, (1980).
7. J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, U.K., (1984).
8. S. Dafermos, Exchange price equilibrium and variational inequalities, Math. Programming 46, 391-402, (1990).
9. X.P. Ding, Generalized strongly nonlinear quasi variational inequalities, J. Math. Anal. Appl. 173, 577-587, (1992).
10. G. Duvaut and J. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, (1976).
11. S.C. Fang and E.L. Peterson, Generalized variational inequalities, J. Optim. Theory Appl. 38, 363-383, (1982).
12. G. Fichera, Problemi elastostatici con vincoli unilaterali: Il problema di Signorini ambigue condizione al contorno, Attm., Acad. Naz. Lincei. Mem. Cl. Sci. Nat. Sez. Ia 7 (8), 91-140, (1963-64).
13. R. Glowinski, J.L. Lions and R. Trémolières, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, (1981).
14. P.T. Marker and J.S. Pang, Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. Programming 48, 161-220, (1990).
15. P. Hartman and G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math 115, 271-310, (1966).
16. C.R. Jou and J.C. Yao, Algorithms for generalized multivalued variational inequalities in Hilbert spaces Computers Math. Applic. 25 (9), 7-16, (1993).
17. A. Karamolegos and D. Kravvaritis, Nonlinear random operators equations and inequalities in Banach spaces Int. J. Math. Math. Sci. 15, 111-118, (1992).
18. N. Kikuchi and J.T. Oden, Contact Problems in Elasticity, SIAM Publishing, Philadelphia, (1988).
19. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, London, (1980).
20. D. Kravvaritis, Nonlinear equations and inequalities in Banach spaces, J. Math. Anal. Appl. 67, 205-214 (1979).
21. D. Kravvaritis, Existence theorems for nonlinear random equations and inequalities, J. Math. Anal. Appl 88, 61-75, (1982).
22. J.L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20, 493-519, (1967).
23. U. Mosco, Implicit variational problems and quasi variational inequalities, In Lecture Notes in Mathematics No. 543, Springer-Verlag, Berlin, (1976).
24. M.A. Noor, Theory of variational inequalities, Lecture Notes, Mathematics Department, King Saud University, Riyadh, (1996).
25. M.A. Noor, Riesz-Fréchet Theorem and monotonicity, M.Sc. Thesis, Queen's University, Kingston, Ontario (1971).
26. M.A. Noor, On variational inequalities, Ph.D. Thesis, Brunel University, London, (1975).
27. M.A. Noor, Strongly nonlinear variational inequalities, C.R. Math. Rep. Acad. Sci. Canada 4, 213-218, (1982).
28. M.A. Noor, An iterative scheme for a class of quasi variational inequalities, J. Math. Anal. Appl. 110, 463-468, (1985).
29. M.A. Noor, An iterative algorithm for variational inequalities, J. Math. Anal. Appl. 158, 448-455, (1991).
30. M.A. Noor, Iterative algorithms for nonlinear variational inequalities, PanAmer. Math. J. 3 (2), 61-80, (1993).
31. M.A. Noor, Wiener-Hopf equations and variational inequalities, J. Optim. Theory Appl. 79, 197-206, (1993).
32. M.A. Noor, Set-valued variational inequalities, Optimization 33, 133-142, (1995).
33. M.A. Noor, Set-valued quasi variational inequalities, PanAmer. Math. J. 5 (2), 83-94, (1995).
34. M.A. Noor, Generalized multivalued variational inequalities, Dynamic Systems and Appl. 4, 469-476, (1995).
35. M.A. Noor, Generalized multivalued variational inequalities (II), Computers Math. Applic. 30 (11), 83-89, (1995).
36. M.A. Noor, Multivalued strongly nonlinear variational inequalities, Optimization 36, 31-39, (1996).
37. M.A. Noor, Multivalued strongly nonlinear quasi variational inequalities, Chinese J. Math. 23 (3), 275-286, (1995).
38. M.A. Noor and W. Oettli, On general nonlinear complementarity problems and quasi-equilibria, Le Matematiche 49, 313-331, (1994).
39. M.A. Noor, K.I. Noor and Th.M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math. 47, 285-312, (1993).
40. M.A. Noor, K.I. Noor and Th.M. Rassias, Invitation to variational inequalities, In Analysis, Geometry and Groups: A Riemann Legacy Volume, (Edited by H.M. Srivastava and Th.M. Rassias), pp. 373-448, Hadronic Press, U.S.A., (1993).
41. A. Pitonyak, P. Shi and M. Shillor, On an iterative method for variational inequalities, Numer. Math. 58, 231-244, (1990).
42. J.F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland, Amsterdam, (1987).
43. P. Shi, Equivalence of variational inequalities with Wiener-Hopf equations, Proc. Amer. Math. Soc. 111, 339-346, (1991).
44. P. Shi, An iterative method for obstacles problems via Green's functions, Nonlinear Analysis 15, 339-344, (1990).
45. M.H. Shih and K.K. Tan, Browder-Hartman-Stampacchia variational inequalities for multivalued monotone operators, J. Math. Anal. Appl. 134, 431-440, (1988).
46. F.O. Speck, General Wiener-Hopf Factorization Methods, Pitman Advanced Publishing Program, London, (1985).
47. G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, C.R. Acad. Sci. Paris 258, 4413-4416, (1964).
48. L.C. Zeng, Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasi variational inequalities, Appl. Math. Mechanics 15, 1069-1080, (1994).