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Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets

Received: 5 April 2015     Accepted: 9 April 2015     Published: 17 June 2015
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Abstract

In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Chowdhury and Tan’s generalized version [1] of Ky Fan’s minimax inequality [2] as the main tool.

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)

DOI 10.11648/j.ajam.s.2015030301.18
Page(s) 46-53
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Generalized Quasi-Variational Inequalities, Pseudo-Monotone Type III Operators, Locally Convex Topological Vector Spaces

References
[1] Mohammad S. R. Chowdhury and K.-K. Tan, Generalization of Ky Fan’s minimax inequality with applications to generalized variational inequalities for pseudo-monotone operators and fixed point theorems, J. Math. Anal. Appl. 204 (1996), 910-929.
[2] K. Fan, A minimax inequality and applications, in “Inequalities, III” (O. Shisha, Ed.), pp.103-113, Academic Press, San Diego, 1972.
[3] D. Chan and J. S. Pang, The generalized quasi-variational inequality problem, Math. Oper. Res. 7(1982), 211-222.
[4] M.-H. Shih and K.-K. Tan, Generalized quasivariational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl., 108 (1985), 333-343.
[5] Mohammad S. R. Chowdhury and E. Tarafdar, Hemi-continuous operators and some applications, Acta Math. Hungar. 83(3) (1999), 251-261.
[6] Mohammad S. R. Chowdhury, The surjectivity of upper-hemi-continuous and pseudo-monotone type II operators in reflexive Banach Spaces, Ganit: J. Bangladesh Math. Soc. 20 (2000), 45-53.
[7] W. Takahashi, Nonlinear variational inequalities and fixed point theorems, Journal of the Mathematical Society of Japan, 28 (1976), 168-181.
[8] M.-H. Shih and K.-K. Tan, Generalized bi-quasi-variational inequalities, J. Math. Anal. Appl., 143 (1989), 66-85.
[9] H. Kneser, Sur un théorème fondamental de la théorie des jeux, C. R. Acad. Sci. Paris, 234 (1952), 2418-2420.
[10] J. P. Aubin, Applied Functional Analysis, Wiley-Interscience, New York, 1979.
[11] J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
[12] R. T. Rockafeller, Convex Analysis, Princeton Univ., Princeton, 1970.
[13] Mohammad S. R. Chowdhury and Kok-Keong Tan, Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasi-variational inequalities on non-compact sets, Proc. Amer. Math. Soc. 3(10) (1998), 2957-2968.
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  • APA Style

    Mohammad S. R. Chowdhury, Yeol Je Cho. (2015). Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets. American Journal of Applied Mathematics, 3(3-1), 46-53. https://doi.org/10.11648/j.ajam.s.2015030301.18

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    ACS Style

    Mohammad S. R. Chowdhury; Yeol Je Cho. Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets. Am. J. Appl. Math. 2015, 3(3-1), 46-53. doi: 10.11648/j.ajam.s.2015030301.18

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    AMA Style

    Mohammad S. R. Chowdhury, Yeol Je Cho. Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets. Am J Appl Math. 2015;3(3-1):46-53. doi: 10.11648/j.ajam.s.2015030301.18

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  • @article{10.11648/j.ajam.s.2015030301.18,
      author = {Mohammad S. R. Chowdhury and Yeol Je Cho},
      title = {Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {3-1},
      pages = {46-53},
      doi = {10.11648/j.ajam.s.2015030301.18},
      url = {https://doi.org/10.11648/j.ajam.s.2015030301.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.18},
      abstract = {In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Chowdhury and Tan’s generalized version [1] of Ky Fan’s minimax inequality [2] as the main tool.},
     year = {2015}
    }
    

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    T1  - Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets
    AU  - Mohammad S. R. Chowdhury
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    DO  - 10.11648/j.ajam.s.2015030301.18
    T2  - American Journal of Applied Mathematics
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    AB  - In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Chowdhury and Tan’s generalized version [1] of Ky Fan’s minimax inequality [2] as the main tool.
    VL  - 3
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Author Information
  • Department of Mathematics, University of Management and Technology, Lahore, Pakistan

  • Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Korea

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