Resolvent equations for set-valued mixed variational inequalities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 42, Issue 1, 2000, Pages 71-83

  Noor, Muhammad Aslam ^a   Rassias, Themistocles M ^b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; SENSITIVITY ANALYSIS; SET THEORY; THEOREM PROVING;

HERATIVE ALGORITHMS; HILBERT SPACE; RESOLVENT EQUATIONS; RESOLVENT OPERATOR; VARIATIONAL INEQUALITY THEORY; WIENER-HOPF EQUATIONS;

VARIATIONAL TECHNIQUES;

EID: 0034274730     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00332-0     Document Type: Article

References (27)

1. S. Adly, W. Oettli, Solvability of Generalized Nonlinear Symmetric Variational Inequalities, University of Mannheim, Germany, Preprint.
2. H. Attouch, M. Théra, A general duality principle for the sum of two operators, J. Convex Anal. 3 (1996) 1-24.
3. C. Baiocchi, A. Capelo, Variational and Quasi-Variational Inequalities, Wiley, New York, 1984.
4. H. Brezis, Operateur Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
5. F. Browder, Convergence to fixed points of nonexpansive nonlinear mappings in Banach Spaces, Arkive Rational Mech. Anal. 24 (1967) 82-90.
6. R.W. Cottle, F. Giannessi, J.L. Lions, Variational Inequalities: Theory and Applications, Wiley, New York, 1980.
7. V.F. Demyanov, G.E. Stavroulakis, L.N. Polyakova, P.D. Panagiotopoulos, Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics, Kluwer Academic Publications, Holland, 1996.
8. F. Giannessi, A. Maugeri, Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, 1995.
9. R. Glowinski, J. Lions, R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, 1981.
10. P.T. Harker, J.S. Pang, Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. Program. 48 (1990) 161-220.
11. A. Hassouni, A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185 (1996) 706-712.
12. A. Moudafi, M. Théra, Finding a zero of the sum of two maximal monotone operators, J. Optim. Theory Appl. 94 (1997) 425-448.
13. M.A. Noor, On Variational Inequalities, Ph.D. Thesis, Brunel University, London, UK 1975.
14. M.A. Noor, Sensitivity analysis of quasi variational inequalities, J. Optim. Theory Appl. 95(2) (1997) 399-407.
15. M.A. Noor, Generalized mixed variational inequalities and resolvent equations, Positivity 1 (1997) 145-154.
16. M.A. Noor, Some recent advances in variational inequalities, Part I, basic concepts, New Zealand J. Math. 26 (1997) 53-80.
17. M.A. Noor, Some recent advances in variational inequalities, Part II, other concepts, New Zealand J. Math. 26 (1997) 229-255.
18. M.A. Noor, Resolvent equations technique for variational inequalities, K. J. Comput. Appl. Math. 4 (1997) 347-358.
19. M.A. Noor, K.I. Noor, Th.M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993) 285-312.
20. M.A. Noor, K.I. Noor, Th.M. Rassias, Set-valued resolvent equations and mixed variational inequalities, J. Math. Anal. 220 (1998) 741-759.
21. M.A. Noor, K.I. Noor, Multi-valued variational inequalities and resolvent equations, Math. Comput. Modelling 26(7) (1997) 109-121.
22. M.A. Noor, On generalized monotone mixed variational inequalities, Math. Computer Modelling (1999), in press.
23. S.M. Robinson, Normal maps induced by linear transformations, Math. Oper. Res. 17 (1992) 691-714.
24. S.M. Robinson, Sensitivity analysis of variational inequalities by normal maps technique, in: F. Giannessi, A. Maugeri (Eds.), Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, 1995, pp. 257-269.
25. P. Shi, Equivalence of variational inequalities with Wiener-Hopf equations, Proc. Amer. Math. Soc. 111 (1991) 339-346.
26. G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, C.R. Acad. Sci. Paris 258 (1964) 4413-4416.
27. D.L. Zhu, P. Marcotte, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities, SIAM J. Optim. 6 (3) (1996) 714-726.