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A Classes of Variational Inequality Problems Involving Multivalued Mappings

Received: 5 January 2018     Accepted: 17 January 2018     Published: 24 February 2018
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Abstract

The main objective of the Variational inequality problem is to study some functional analytic tools, projection method and fixed point theorems and then exploiting these to study the existence of solutions and convergence analysis of iterative algorithms developed for some classes of Variational inequality problem. The main objective of this paper is to study the existence of solutions of some classes of Variational inequalities using fixed point theorems for multivalued and using Banach contraction theorem we prove the existence of a unique solution of multi value Variational inequality problem.

Published in Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 1)
DOI 10.11648/j.sjams.20180601.15
Page(s) 43-48
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), 2018. Published by Science Publishing Group

Keywords

Fixed Points Theorems, Variational Inequality Problems, Strongly Lipschitz Operator

References
[1] Baiocchi, C. and Capelo, A. Variational and qualities, Applications to free boundary problem, John Wiley and Sons, New York 1984.
[2] Cottle, R. W. Giannessi, F. and Lions, J. L, Variational inequalities and complementarity problems, Theory and applications, John Wiley and Sons, New York.
[3] Duvaut, G, and Lions, J. L. Inequalities in mechanics and physics, Springer Verlag, Berlin, 1976.
[4] Eilenberg S. and Montgomery D. Fixed point theorem for multivalued transformations, Amer. J. Math (1946).
[5] Ekland, I, and Temam, R,. Convex analysis and Variational inequalities, North Holland, Amsterdam, 1976.
[6] Hlavacak, I, Haslinger, J, and Necas. J., Solutions of Variational inequalities in mechanics, Springer Verlag, New York, 1988.
[7] Khalil Ahmad, K. R. Kazmi and Z. A. Siddiqui, On a class of Generalized Variational Inequalities, Indian. J. Pure app. Math 28 (4): 487-499. April 1997.
[8] Mircea, S. and Analuzia, M, Variational inequalities with applications, study of antiplane frictional contact problems, Springer.
[9] Ram U. Verma, Generalized nonlinear Variational inequality problems involving Multivalued Mappings, Journal of Applied Mathematics and Stochastic Analysis, (1997), 289-295.
[10] Rudin W, Principles of mathematical analysis, McGraw-Hill Book Co, New York, 1964.
[11] Ram U. Verma, Generalized Nonlinear Variational Inequality Problems Involving Multivalued Mapping, Journal of Applied Mathematics and Stochastic Analysis, 10-3 (1997), 289-295.
[12] 8. Noor, MA, Noor, KI: On general quasi-variational inequalities. J. King Saud Univ., Sci. 24, 81-88 (2012).
[13] John F. Smith Memorial Professor, Virtual Center for Supernetworks, Variational Inequalities, Networks, and Game Theory, Spring 2014.
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  • APA Style

    Nedal Hassan Elbadowi Eljaneid. (2018). A Classes of Variational Inequality Problems Involving Multivalued Mappings. Science Journal of Applied Mathematics and Statistics, 6(1), 43-48. https://doi.org/10.11648/j.sjams.20180601.15

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    ACS Style

    Nedal Hassan Elbadowi Eljaneid. A Classes of Variational Inequality Problems Involving Multivalued Mappings. Sci. J. Appl. Math. Stat. 2018, 6(1), 43-48. doi: 10.11648/j.sjams.20180601.15

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    AMA Style

    Nedal Hassan Elbadowi Eljaneid. A Classes of Variational Inequality Problems Involving Multivalued Mappings. Sci J Appl Math Stat. 2018;6(1):43-48. doi: 10.11648/j.sjams.20180601.15

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  • @article{10.11648/j.sjams.20180601.15,
      author = {Nedal Hassan Elbadowi Eljaneid},
      title = {A Classes of Variational Inequality Problems Involving Multivalued Mappings},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {6},
      number = {1},
      pages = {43-48},
      doi = {10.11648/j.sjams.20180601.15},
      url = {https://doi.org/10.11648/j.sjams.20180601.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20180601.15},
      abstract = {The main objective of the Variational inequality problem is to study some functional analytic tools, projection method and fixed point theorems and then exploiting these to study the existence of solutions and convergence analysis of iterative algorithms developed for some classes of Variational inequality problem. The main objective of this paper is to study the existence of solutions of some classes of Variational inequalities using fixed point theorems for multivalued and using Banach contraction theorem we prove the existence of a unique solution of multi value Variational inequality problem.},
     year = {2018}
    }
    

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    AU  - Nedal Hassan Elbadowi Eljaneid
    Y1  - 2018/02/24
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    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - The main objective of the Variational inequality problem is to study some functional analytic tools, projection method and fixed point theorems and then exploiting these to study the existence of solutions and convergence analysis of iterative algorithms developed for some classes of Variational inequality problem. The main objective of this paper is to study the existence of solutions of some classes of Variational inequalities using fixed point theorems for multivalued and using Banach contraction theorem we prove the existence of a unique solution of multi value Variational inequality problem.
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Author Information
  • Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk, Kingdom of Saudi Arabia

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