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A Class of Generalized Operator Quasi-Equilibrium Problems

Received: 24 January 2021     Accepted: 15 February 2021     Published: 26 March 2021
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Abstract

In this work, introduce and study a generalized operator quasi-equilibrium problems (in short, OQEP) in the setting of topological vector spaces. We prove some new existence results for the solution of this problem by applying C(f)-quasiconvex, escaping sequence in Hausdörff topological vector spaces. The results of this paper can generalize and unify previously known corresponding results of this area.

Published in American Journal of Applied Mathematics (Volume 9, Issue 1)
DOI 10.11648/j.ajam.20210901.13
Page(s) 16-19
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), 2021. Published by Science Publishing Group

Keywords

Operator Quasi-equilibrium Problem, C(f)-quasiconvex, Escaping Sequence

References
[1] Ansari, Q. H. and Yao, J. C., An existence result for the generalized vector equilibrium problem, Appl. Math. Letters 12 (1999), 53-56.
[2] Blum, E. and Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Stud. 63 (1994), 123-145.
[3] Ding, X.P., Kim, W.K. and Tan, K.K., Equilibria of non-compact generalized game with L∗-majerized preferences, J. Math. Anal. Appl. 164 (1992), 508-517.
[4] Ding, X.P., Kim, W.K. and Tan, K.K., Equilibria of non-compact generalized game with L-majerized correspendences, International J. Math. & Math. Sci. 17 (1994), 783-790.
[5] Domokos, A and Kolumbán, J., Variational inequalities with operator solutions, J. Global. Optim. 23 (2002), 99-110.
[6] Khaliq, A., On generalized vector equilibrium problems, Gaint 19 (1999), 69-83.
[7] Khaliq, A. and Krishan, S., Vector quasi-equilibrium problems Bull. Austral. Math. Soc., 68 (2003), 295-302.
[8] Khaliq, A. and Raouf, A., Geeneralized vector quasi- equilibrium problems, Adv. Nonl. Vari. Ineq. 7 (1) (2004), 47-57.
[9] Khaliq, A. and Raouf, A., Existence of solutions for generalized vector variational-like inequalities, South East Asian J. Math. & Math. Sc. 2 (1) (2003), 1-14.
[10] Kazmi, K. R., A variational principle for vector equilibrium problems, Proc. Indian Acad. Sci. (Math. Sci ), 111 (2001), 465-470.
[11] Kazmi, K. R., On vector equilibrium problem, Proc. Indian Acad. Sci., 110 (2000), 213-223.
[12] Kazmi, K. R. and Raouf, A., A class of operator equilibrium problem, J. Math. Annl. and Appl. 308 (2005), 554-564.
[13] Kazmi, K. R. and Raouf, A., Preturbed Operator Equilibrium Problems South East Asian J. Math. & Math. Sc. 8 (1) (2009), 91-100.
[14] Kim, J. K. and Raouf, A., A Class of Generalized Operator Equilibrium Problems Filomat 31: 1 (2017) 1-8.
[15] Qun, L., Generalized vector variational-like inequalities, In: Vector Variational Inequalities and Vector Equilibria, pp. 363-369, Nonconvex Optim. Appl. Vol. 38, Kluwer Acad. Publ. Dordrecht, 2000.
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  • APA Style

    Abdul Raouf, Rajesh Kumar Gupta, Shivani Sharma. (2021). A Class of Generalized Operator Quasi-Equilibrium Problems. American Journal of Applied Mathematics, 9(1), 16-19. https://doi.org/10.11648/j.ajam.20210901.13

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    ACS Style

    Abdul Raouf; Rajesh Kumar Gupta; Shivani Sharma. A Class of Generalized Operator Quasi-Equilibrium Problems. Am. J. Appl. Math. 2021, 9(1), 16-19. doi: 10.11648/j.ajam.20210901.13

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    AMA Style

    Abdul Raouf, Rajesh Kumar Gupta, Shivani Sharma. A Class of Generalized Operator Quasi-Equilibrium Problems. Am J Appl Math. 2021;9(1):16-19. doi: 10.11648/j.ajam.20210901.13

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  • @article{10.11648/j.ajam.20210901.13,
      author = {Abdul Raouf and Rajesh Kumar Gupta and Shivani Sharma},
      title = {A Class of Generalized Operator Quasi-Equilibrium Problems},
      journal = {American Journal of Applied Mathematics},
      volume = {9},
      number = {1},
      pages = {16-19},
      doi = {10.11648/j.ajam.20210901.13},
      url = {https://doi.org/10.11648/j.ajam.20210901.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210901.13},
      abstract = {In this work, introduce and study a generalized operator quasi-equilibrium problems (in short, OQEP) in the setting of topological vector spaces. We prove some new existence results for the solution of this problem by applying C(f)-quasiconvex, escaping sequence in Hausdörff topological vector spaces. The results of this paper can generalize and unify previously known corresponding results of this area.},
     year = {2021}
    }
    

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    T1  - A Class of Generalized Operator Quasi-Equilibrium Problems
    AU  - Abdul Raouf
    AU  - Rajesh Kumar Gupta
    AU  - Shivani Sharma
    Y1  - 2021/03/26
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    N1  - https://doi.org/10.11648/j.ajam.20210901.13
    DO  - 10.11648/j.ajam.20210901.13
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20210901.13
    AB  - In this work, introduce and study a generalized operator quasi-equilibrium problems (in short, OQEP) in the setting of topological vector spaces. We prove some new existence results for the solution of this problem by applying C(f)-quasiconvex, escaping sequence in Hausdörff topological vector spaces. The results of this paper can generalize and unify previously known corresponding results of this area.
    VL  - 9
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Government Degree College Mendhar, Topa, Jammu and Kashmir, India

  • Department of Mathematics, Lovely Professional University, Punjab, India

  • Department of Mathematics, Lovely Professional University, Punjab, India

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