GENERALIZED SET-VALUED MIXED NONLINEAR QUASI VARLIATIONAL INEQUALITIES

  • H, M-U (Department of mathematics College of Science king Saud University)
  • 발행 : 1998.03.01

초록

In this paper we introduce and study a number of new classes of quasi variational inequalities. using essentially the projection technique and its variant forms we prove that the gen-eralized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations(normal maps). This equivalence enables us to suggest a number of iterative algorithms solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational in-equalities we obtain a class of quasi variational inequalities studied by Siddiqi Husain and Kazmi [35] but there are several inaccuracies in their formulation of the problem the statement and the proofs of the problem the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of thir results can be obtained as special cases from our main results.

키워드

참고문헌

  1. Variational and Quasi Variational Inequalities C.Baiocchi;A.Capelo
  2. Applications des Inequations Variationelles en Control et en Stochastiques A.Bensoussan;J.L.Lions
  3. Math. Oper. Research v.7 The generalized quasi variational inequality problems D.Chan;J.S.Pang
  4. The Linear Complementarity problems R.W.Cottle;J.S.Pang;R.E.Stone
  5. Free and Moving Boundary Problems J.Crank
  6. Set-Valued Analysis v.1 An extension theorem for generalized quasi variational inequalities P.Cubiotti
  7. Computers Math. Applic v.28 no.4 The generalized quasi variational inequality problem over non-compact sets P.Cubiotti;C.Yao
  8. Math. Programming v.46 Exchange price equilibrium and variational inequalities S.Dafermos
  9. J. Math. Anal. Appl. v.173 Generalized strongly nonlinear quasi variational inequalities X.P.Ding
  10. Numerical Analysis of Variational Inequalities R.Glowinski;J.L.Lions;R.Tremolieres
  11. Mathematical Programming v.48 Finite dimensional variational inequality and non-linear complementarity problems: a survey of theory, algorithms and applications P.T.Harker;J.S.Pang
  12. Computers Math. Appl. v.25 no.9 Algorithms for generalized multivalued variational inequalities in Hilbert spaces C.R.Jou;Y.C.Yao
  13. Contact Problems in Elasticity N.Kikuchi;J.T.Oden
  14. J. Math. Anal. Appl. v.88 Existence theorems for nonlinear random equations and inequalities D.Kravvaritis
  15. Lect. Notes Math. v.543 Implicit variational problems and quasi variational inequalities U.Mosco
  16. Optimization v.33 Set-valued variational inequalities M. Aslam Noor
  17. Ph. D. Thesis, Brunel University On Variational Inequalities M. Aslam Noor
  18. PanAmer. Math. J. v.3 no.2 Iterative algorithms for nonlinear variational inequalities M. Aslam Noor
  19. J. Math. Anal. Appl. v.128 On a class of variational inequalities M. Aslam Noor
  20. Optimization v.36 Multivalued strongly nonlinear variational inequalities M. Aslam Noor
  21. PanAmer. Math. J. v.2 no.4 Generalized Wiener-Hopf equations and nonlinear quasi variational inequalities M. Aslam Noor
  22. New Zealand J. Math. v.26 no.2;4 Some recent advances in variational inequalities (Ⅰ,Ⅱ) M. Aslam Noor
  23. Computers Math. Appl. Generalized multivalued quasi variational inequalities (Ⅱ) M. Aslam Noor
  24. Optimization v.37 General nonlinear mixed variational-like inequalities M. Aslam Noor
  25. Theory of variational inequalities, Lecture Notes M. Aslam Noor
  26. J. Comput. Appl. Math. v.47 Some aspects of variational inequalities M. Aslam Noor;K. Inayat Noor;Th.M. Rassias
  27. Analysis, Geometry and Groups: A Riemann Legacy Volume Invitation to variational inequalities M. Aslam Noor;K.Inayat Noor;Th.M.Rassias;H.M.Srivastava(ed.);Th.M.Rassias(ed.)
  28. Le Matematiche v.49 On general nonlinear complementarity problems and quasi-equilibria M. Aslam Noor;W.Oettli
  29. Math. Computer Modelling Multivalued variational inequalities and resolvent equations M. Aslam Noor;K. Inayat Noor
  30. Numer. Math. v.58 On an iterative method for variational inequalities A.Pitonyak;P.Shi;M.Shillor
  31. Math. Opers. Research v.17 Normal maps induced by linear transformations S.M.Robinson
  32. Obstacle Problems in Mathematical Physics J.F.Rodrigue
  33. Proc. Amer. Math. Soc. v.111 Equivalence of variational inequalities with Wiener-Hopf equations P.Shi
  34. Nonlinear Analysis v.15 An iterative method for obstacle problems via Green's functions P.Shi
  35. Mem. Fac. Sci. Kochi University (Math) v.16 Generalized mixed quasi variational inequalities in Hilbert spaces A.H.Siddiqi;S.Husain;Kazmi
  36. J. Math. Anal. Appl. v.144 An algorithm for a class of quasi variational inequalities A.H.Siddiqui;Q.H.Ansari
  37. General Wiener-Hopf Factorization Methods F.O.Speck
  38. C.R. Acad. Sci. Paris v.258 Formes bilineaires coercitives sur les ensembles convexes G.Stampacchia