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GENERALIZED SET-VALVED STRONGLY NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES

Cho, Y.J.   (Department of Mathematics Gyeongsan national University  ); Fang, Y.P.    (Department of Mathemetics Sichuan University   ); Huang, N.J.   (Department of Mathemetics Sichuan UniversityUU0016783  ); Kim, K.H.    (Department of Mathematics Gyeongsan national University  );
  • 초록

    In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma [16], [17] as special cases.


  • 주제어

    strongly nonlinear variational inequality .   set valued-mapping .   generalized monotone type mapping .   generalized Lipschitzian type mapping .   the KKm mapping.  

  • 참고문헌 (20)

    1. Sensitivity analysis for strongly nonlinear quasi-variational inclusions , R. P. Agarwal;Y. J. Cho;N. J. Huang , Appl. Math. Lett. / v.13,pp.19-24,
    2. Generalized nonlinear implicit quasi-variational inclusion and an application to implicit variational inequalities , N. J. Huang , Z. Angew. Math. Mech. / v.79,pp.569-575,
    3. Generalized nonlinear mixed quasi-variational inequalities , N. J. Huang;M. R. Bai;Y. J. Cho;S. M. Kang , Computers Math. Appl. / v.40,pp.205-215,
    4. A new class of generalized nonlinear mixed quasi-variational inequalities in Banach spaces , N. J. Huang;Y. P. Fang;Y. J. Cho , Math. Inequal. Appl. / v.,pp.,
    5. G. X. Z. Yuan , KKM Theory and Applications / v.,pp.,
    6. On the generalized set-valued strongly nonlinear implicit variational inequalities , N. J. Huang;Y. P. Liu;Y. Y. Tang;M. R. Bai , Computers Math. Appl. / v.37,pp.29-36,
    7. Modified projection-type methods for monotone variational inequalities , M. V. Solodov;P. Tseng , SIAM J. Control. Optim. / v.34,pp.1814-1836,
    8. On monotone nonlinear variational inequality problems , R. U. Verma , Comment. Math. Univ. Carolinae / v.39,pp.91-98,
    9. On the generalized implicit quasi-variational inequalities , N. J. Huang , J. Math. Anal. Appl. / v.216,pp.197-210,
    10. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , P. T. Harker;J. S. Pang , Math. Programming / v.48,pp.161-220,
    11. F. Giannessi;A. Maugeri , Variational Inequalities and Network Equilibrium Problems / v.,pp.,
    12. Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities , N. J. Huang;C. X. Deng , J. Math. Anal. Appl. / v.256,pp.345-359,
    13. Random generalized set-valued strongly nonlinear implicit quasi-variational inequalities , Y. J. Cho;N. J. Huang;S. M. Kang , J. Inequal. Appl. / v.5,pp.515-531,
    14. Generalized set-valued variational inclusions in Banach spaces , S. S. Chang;Y. J. Cho;B. S. Lee;I. H. Jung , J. Math. Anal. Appl. / v.246,pp.409-422,
    15. E. Zeidler , Nonlinear Functional Analysis and Its Applications Ⅳ / v.,pp.,
    16. Nonlinear variational inequalities on convex subsets of Banach spaces , R. U. Verma , Appl. Math. Lett. / v.10,pp.25-27,
    17. Some properties of convex sets related to fixed point theorem , K. Fan , Math. Annal. / v.266,pp.519-537,
    18. A new completely general class of variational inclusions with noncompact valued mappings , N. J. Huang , Computers Math. Appl. / v.35,pp.9-14,
    19. Generalized pseudo-contractions and nonlinear variational inequalities , R. U. Verma , Publ. Math. Debrecen / v.53,pp.23-28,
    20. P. D. Panagiotopoulos , Inequality Problems in Mechanics and Applications / v.,pp.,

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