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Existence of solutions for generalized quasi-variational-like inequalities

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Abstract

In this paper, some existence theorems of solutions for a class of generalized quasi-variational-like inequalities with discontinuous mappings are proved under paracompact setting in topological vector spaces. These theorems unify, improve and generalize many recent results.

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References

  1. J. P. Aubin and I. Ekeland,Applied Nonlinear Analysis, John Wiley & Sons, New York (1984).

    MATH  Google Scholar 

  2. C. Baiocchi and A. Capelo.Variational and Quasi-variational Inequalities. John Wiley & Sons, New York (1984).

    Google Scholar 

  3. D. Kinderlehrer and G. Stampacchi,An Introduction to Variational Inequalities, Acad. Press, New York (1980).

    MATH  Google Scholar 

  4. D. Chan and J. S. Pang. The generalized quasi-variational inequalities,Math. Oper. Res.,7 (1982), 211–222.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. T. Harker and J. S. Pang. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications,Math. Program, Ser B.48 (1990), 161–220.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. A. Noor. General variational inequalities.Appl. Math. Lett.,1 (1988), 119–122.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. A. Noor, General algorithm and sensitivity for variational inequalities,J. Appl. Math. Stoch. Anal.,5 (1992), 29–42.

    MATH  MathSciNet  Google Scholar 

  8. M. A. Noor, K. I. Noor and T. M. Rassias, Some aspects of variational inequalities,J. Comput. Appl. Math.,47 (1993), 285–312.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. C. Yao, General variational inequalities in Banach spaces,Appl. Math. Lett.,5, 1 (1992), 51–54.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. C. Yao, On the general variational inequalities,J. Math. Anal. Appl.,174 (1993), 550–555.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. C. Yao and J. S. Guo, Variational and generalized variational inequalities with discontinuous mappings,J. Math. Anal. Appl.,182 (1994), 371–392.

    Article  MATH  MathSciNet  Google Scholar 

  12. X. P. Ding and E. Tarafdar, Generalized nonlinear variational inequalities with non-monotone set-valued mappings,Appl. Math. Lett.,7, 4 (1994), 5–11.

    Article  MATH  MathSciNet  Google Scholar 

  13. X. P. Ding A class of generalized variational inequalities and its applications,J. Sichuan Normal Univ.,17, 6 (1994), 10–16. (in Chinese)

    Google Scholar 

  14. X. P. Ding Existence of solutions for a class of generalized variational inequalities,J. Yantai Univ.,2 (1995), 15–22. (in Chinese)

    MATH  Google Scholar 

  15. X. P. Ding Implicit variational inequalities with discontinuous mappings.J. Sichuan Normal Univ.,18, 2 (1995), 8–15. (in Chinese)

    Google Scholar 

  16. J. Parida, M. Sahoo and A. Kumar, A variational-like inequality problem,Bull. Austral. Math. Soc.,39 (1989), 225–231.

    MATH  MathSciNet  Google Scholar 

  17. N. H. Dien, Some remarks on variational-like inequalities.Bull. Austral. Math. Soc.,46 (1992), 335–342.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. H. Siddiqi, A. Khaliq and Q. H. Ansari, On variational-like inequalities.Am. Sci. Math. Québec. 18, 1 (1994), 95–104.

    MATH  MathSciNet  Google Scholar 

  19. X. P. Ding Quasi-variational inequalities and social equilibrium.Appl. Math. and Mech. (English Ed.),12, 7 (1991), 639–646.

    MATH  Google Scholar 

  20. W. W. Hogan. Point-to-set maps in mathematical programming.SIAM Rev.,15 (1973), 591–603.

    Article  MATH  MathSciNet  Google Scholar 

  21. M. H. Shih and K. K. Tan, Covering theorems of convex sets related fixed point theorems, inNonlinear and Convex Analysis, Marcel Dekker Inc., New York, (1987), 235–244.

    Google Scholar 

  22. J. X. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities,J. Math. Anal. Appl.,132 (1988). 213–225.

    Article  MATH  MathSciNet  Google Scholar 

  23. H. Kneser. Sur un théoème fondamantal de la théorie des jeux.C. R. Acad. Sci., Paris,234 (1952), 2418–2420.

    MathSciNet  Google Scholar 

  24. J. C. Yao, Gemeralized-quasi-variational inequality problems with discontinuous mappings,Math. Oper. Res.,20, 2 (1995), 465–478.

    MATH  MathSciNet  Google Scholar 

  25. O. H. Merrill, Applications and extensions of an algorithm that computes fixed points of certain upper semicontinuous point-to-set mappings, Ph. D Thesis. Univ. of Michigan, Ann Arbor, MI. (1972).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, 610066, Chengdu, P. R. China

    Ding Xieping

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  1. Ding Xieping
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Project supported by the National Natural Science Foundation of China

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Xieping, D. Existence of solutions for generalized quasi-variational-like inequalities. Appl Math Mech 18, 141–150 (1997). https://doi.org/10.1007/BF02458013

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  • DOI: https://doi.org/10.1007/BF02458013

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