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Random Completely Generalized Set-Valued Implicit Quasi-Variational Inequalities

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Abstract

The purpose of this paper is to introduce a class of new random completely generalized set-valued implicit quasi-variational inequalities, to construct new random iterative algorithms, and to give some existence theorems of random solutions for this class of random completely generalized set-valued implicit quasi-variational inequalities. We also prove the convergence of random iterative sequences generated by the algorithms. Our results extend and improve the earlier and recent results.

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References

  1. Baiocchi, C. and Capelo, A.: Variational and quasi-variational inequalities, Applications to Free Boundary Problems Wiley, New York (1984).

    Google Scholar 

  2. Bensoussan, A.: Stochastic control by functional analysis method, North-Holland, Amsterdam (1982).

    Google Scholar 

  3. Bensoussan, A., Goursat, M. and Lions, J. L.:Control impulsinnel et inequations quasi-variat-ionnelles stationaries, C. R. Acad. Sci. 276(1973) 1279-1284.

    Google Scholar 

  4. Bensoussan, A. and Lions, J. L.: Impulse control and quasi-variational inequalities, Gauthiers-Villers, Bordas, Paris (1984).

    Google Scholar 

  5. Chang, S. S.: Variational inequality and complementarity problem theory with applications, Shanghai Scientific and Tech. Literature Publishing House, Shanghai (1991).

    Google Scholar 

  6. Chang, S. S.: Fixed Point Theory with Applications, Chongqing Publishing House, Chongqing (1984).

    Google Scholar 

  7. Chang, S. S. and Huang, N. J.: Generalized random multivalued quasi-complementarity problems, Indian J. Math. 35(1993) 305-320.

    Google Scholar 

  8. Chang, S. S. and Huang, N. J.: Random generalized set-valued quasi-complementarity problem, Acta Math. Appl. Sinica 16(1993) 396-405.

    Google Scholar 

  9. Chang, S. S. and Zhu, Y. G.: On the problems for a class of random variational inequalities and random quasi-variational inequalities, J. Math. Res. Exposition 9(1989) 385-393.

    Google Scholar 

  10. Himmelberg, C. J.: Measurable relations, Fund. Math. 87(1975) 53-72.

    Google Scholar 

  11. Huang, N. J.: On the generalized implicit quasivariational inequalities, J. Math. Anal. Appl. 216(1997) 197-210.

    Google Scholar 

  12. Huang, N. J.: Random general set-valued strongly nonlinear quasi-variational inequalities,J. Sichuan University 31(1994) 420-425.

    Google Scholar 

  13. Huang, N. J.: Random generalized setvalued implicit variational inequalities, J. Liaoning Normal University 18(1995) 89-92.

    Google Scholar 

  14. Huang, N. J. and Cho, Y. J.: Random completely generalized nonlinear variational inclusions, Far East J. Math. Sci. Special Volume(1998) Part I, 93-106.

  15. Huang, N. J., Long, X. and Cho, Y. J.: Random completely generalized nonlinear variational inclusion with non-compact valued random mappings, Bull. Korean Math. Soc. 34(1997) 603-615.

    Google Scholar 

  16. Mosco, U.: Implicit variational problems and quasi-variational inequalities, Lecture Notes in Mathematics, Springer-Verlag, 543(1976) 83-156.

    Google Scholar 

  17. Noor, M. A.: Some recent advances in variational inequalities, PartI, New Zealand J. Math. 26(1) (1997) 53-80.

    Google Scholar 

  18. Noor, M. A.: Some recent advances in variational inequalities, Part II, New Zealand J. Math. 26(4) (1997) 229-255.

    Google Scholar 

  19. Noor, M. A.: An iterative scheme for a class of quasi-variational inequalities,J.Math.Anal. Appl. 110(1985) 463-468.

    Google Scholar 

  20. Noor, M. A. and Elsanousi, S. A.: Iterative methods for random variational inequalities,Pan Amer. Math. J. 3(1) (1993) 39-50.

    Google Scholar 

  21. Siddiqi, A. H. and Ansari, Q. H.: Strongly nonlinear quasi-variational inequalities,J.Math. Anal. Appl. 149(1990) 444-450.

    Google Scholar 

  22. Tan, N. X.: Random quasi-variational inequality, Math. Nachr. 125(1986) 319-328.

    Google Scholar 

  23. Yuan, X. Z.:Non-compact random generalized games and random quasi-variational inequali-ties, J. Appl. Math. Stoch. Anal. 7(1994) 467-486.

    Google Scholar 

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Jing Huang, N., Je Cho, Y. Random Completely Generalized Set-Valued Implicit Quasi-Variational Inequalities. Positivity 3, 201–213 (1999). https://doi.org/10.1023/A:1009784323320

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