DOI QR코드

DOI QR Code

EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERALIZED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • LIU ZEQING (Department of Mathematics Liaoning Normal University) ;
  • GUAN, HONG-YAN (Department of Mathematics Liaoning Normal University) ;
  • SHIM, SOO-HAK (Department of Mathematics and Research Institute of Natural Science Gyeongsang National University) ;
  • KANG, SHIN-MIN (Department of Mathematics and Research Institute of Natural Science Gyeongsang National University)
  • Published : 2005.10.01

Abstract

Keywords

References

  1. R. P. Agarwal, Y. J. Cho, and N. J. Huang, sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett. 13 (2000), no. 6, 19-24
  2. Q. H. Ansari and J. C. Yao, Generalized variational-like inequalities and a gap function, Bull. Austral. Math. Soc. 59 (1999), 33-44 https://doi.org/10.1017/S0004972700032573
  3. Q. H. Ansari and J. C. Yao, Iterative schemes for solving mixed variational-like inequalities, J. Optim. Theory Appl. 108 (2001), 527-541 https://doi.org/10.1023/A:1017531323904
  4. R. K. Bose, On a general nolinear variational inequality, Bull. Austral. Math. Soc. 42 (1990), 399-406 https://doi.org/10.1017/S0004972700028562
  5. S. S. Chang, Generalized strongly nonlinear quasi-complementarity problem in Hilbert spaces, J. Math. Anal. Appl. 158 (1991), 194-202 https://doi.org/10.1016/0022-247X(91)90276-6
  6. O. Chadli and J. C. Yao, On generalized variational-like inequalities, Arch. Math. 80 (2003), 331-336 https://doi.org/10.1007/s00013-003-0482-0
  7. X. P. Ding, General algorithm of solutions for nonlinear variational inequalities in Banach spaces, Comput. Math. Appl. 34 (1997), no. 9, 131-137 https://doi.org/10.1016/S0898-1221(97)00194-6
  8. X. P. Ding, Algorithms of solutions for mixed nonlinear quasi-variational-like inequalities in reflexive Banach spaces, Appl. Math. Mech. 19 (1998), no. 6, 489-496 https://doi.org/10.1007/BF02457791
  9. X. P. Ding, General algorithm for nonlinear variational-like inequalities in reflexive Banach spaces, Indian J. Pure Appl. Math. 29 (1998), no. 2, 109-120
  10. X. P. Ding, Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities, Appl. Math. Comput. 113 (2000), 67-80 https://doi.org/10.1016/S0096-3003(99)00068-5
  11. X. P. Ding, Generalized quasi-variational-like inequalities with nonconvex function-als, Appl. Math. Comput. 122 (2001), 267-282 https://doi.org/10.1016/S0096-3003(00)00027-8
  12. X. P. Ding, Existence aryl algorithm of solutions for nonlinear mixed variational- like inequalities in-Banach. spaces, J. Comput. Appl. Math. 157 (2003), 419-434 https://doi.org/10.1016/S0377-0427(03)00421-7
  13. X. P. Ding and C. L. Luo, Existence and algorithm for solving some generalized mixed implicit variational inequalities, Comput. Math. Appl. 37 (1999), 23-30
  14. Y. P. Fang and N. J. Huang, Variational-like inequalities with generalized monotone mappings in Banach spaces, J. Optim. Theory Appl. 118 (2003), 327-338 https://doi.org/10.1023/A:1025499305742
  15. N. J. Huang, M. R. Bai, Y. J. Cho, and S. M. Kang, Generalized nonlinear mixed quasi-variational inequalities, Computers Math. Applic. 40 (2000), 205-215 https://doi.org/10.1016/S0898-1221(00)00154-1
  16. N. J. Huang and Y. P. Fang, Auxiliary principle technique for generalized setvalued nonlinear quasi-variational-like inequalities, Math. Inequal. Appl. 6(2) (2003), 339-350
  17. B. S. Lee and G. M. Lee, A vector version of Minty's lemma and application, Appl. Math. Lett. 12 (1999), 43-50
  18. B. S. Lee and G. M. Lee, Variational inequalities for $(\eta, \theta)$-pseudomonotone operators in nonre-flexive Banach spaces, Appl. Math. Lett. 12 (1999), 13-17
  19. B. S. Lee, G. M. Lee, and S. J. Lee, Variational-type inequalities for $(\eta, \theta, \delta)$ pseudomonotone-type set-valued mappings in nonreflexive Banach spaces, Appl. Math. Lett. 15 (2002), 109-114 https://doi.org/10.1016/S0893-9659(01)00101-X
  20. B. S. Lee and S. J. Lee, Vector variational-like inequalities for set-valued mappings, Appl. Math. Lett. 13 (2000), 57-62
  21. Z. Liu, L. Debnath, S. M. Kang, and J. S. Ume, Completely generalized multivalued nonlinear quasi-variational inclusions, Internat. J. Math. and Math. Sci. 30 (2002), no. 10, 593-604 https://doi.org/10.1155/S0161171202108283
  22. Z. Liu, L. Debnath, S. M. Kang and J. S. Ume, On the generalized nonlinear quasivariational inclusions, Acta. Math. Informatica Universitatis Ostraviensis, 11 (2003), 81-90
  23. Z. Liu and S. M. Kang, Generalized multivalued nonlinear quasi-variational inclusions, Math. Nachr. 253 (2003), 45-54 https://doi.org/10.1002/mana.200310044
  24. Z. Liu and S. M. Kang, Comments on the papers involving variational and quasi-variational inequalities for fuzzy mappings, Math. Sci. Res. J. 7(10) (2003), 394-339
  25. Z. Liu, S. M. Kang, and J. S. Ume, On general variational inclusions with noncompact valued mappings, Adv. Nonlinear Var. Inequal. 5 (2002), no. 2, 11-25
  26. Z. Liu, S. M. Kang and J. S. Ume, Generalized variational inclusions for fuzzy mappings, Adv. Nonlinear Var. Inequal., 6 (2003), 31-40
  27. Z. Liu, S. M. Kang, and J. S. Ume, Completely generalized multivalued strongly quasivariational inequali-ties, Publ. Math. Debrecen 62 (2003), no. 1-2, 187-204
  28. G. K. Panda and N. Dash, Strongly nonlinear variational-like inequalities, Indian J. pure appl. Math. 31 (2000), 797-808
  29. J. Parida, M. Sahoo, and A. Kumar, A variational-like inequalities problem, Bull. Austral. Math. Soc. 39 (1989), 225-231 https://doi.org/10.1017/S0004972700002690
  30. D. Pascaliand and S. Sburlan, Nonlinear Mapping of Monotone Type, Sijthoff & Noordhoof, The Netherlands. 1978
  31. J. C. Yao, Existence of generalized variational inequalities, Oper. Res. Lett. 15 (1994), 35-40 https://doi.org/10.1016/0167-6377(94)90011-6