Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

Mohammad Chowdhury; Kok-Keong Tan

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 158-169
  • ISSN: 2391-5455

Abstract

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In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.

How to cite

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Mohammad Chowdhury, and Kok-Keong Tan. "Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets." Open Mathematics 8.1 (2010): 158-169. <http://eudml.org/doc/269010>.

@article{MohammadChowdhury2010,
abstract = {In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.},
author = {Mohammad Chowdhury, Kok-Keong Tan},
journal = {Open Mathematics},
keywords = {Generalized bi-quasi-variational inequalities; Quasi-pseudomonotone type II operators; Strongly quasi-pseudo-monotone type II operators; Locally convex Hausdorff topological vector spaces; generalized bi-quasi-variational inequalities; quasi-pseudomonotone type II operators; strongly quasi-pseudo-monotone type II operators; locally convex Hausdorff topological vector spaces},
language = {eng},
number = {1},
pages = {158-169},
title = {Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets},
url = {http://eudml.org/doc/269010},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Mohammad Chowdhury
AU - Kok-Keong Tan
TI - Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 158
EP - 169
AB - In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
LA - eng
KW - Generalized bi-quasi-variational inequalities; Quasi-pseudomonotone type II operators; Strongly quasi-pseudo-monotone type II operators; Locally convex Hausdorff topological vector spaces; generalized bi-quasi-variational inequalities; quasi-pseudomonotone type II operators; strongly quasi-pseudo-monotone type II operators; locally convex Hausdorff topological vector spaces
UR - http://eudml.org/doc/269010
ER -

References

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  1. [1] Aubin J.P., Applied Functional Analysis, Wiley-Interscience, New York, 1979 Zbl0424.46001
  2. [2] Brézis H., Nirenberg L., Stampacchia G., A remark on Ky Fan’s minimax principle, Boll. Un. Mat. Ital. (4), 1972, 6, 293–300 Zbl0264.49013
  3. [3] Chowdhury M.S.R., Tan K.-K., 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., 1996, 204, 910–929 http://dx.doi.org/10.1006/jmaa.1996.0476 
  4. [4] Chowdhury M.S.R., Tan K.-K., Application of upper hemi-continuous operators on generalized bi-quasi-variational inequalities in locally convex topological vector spaces, Positivity, 1999, 3, 333–344 http://dx.doi.org/10.1023/A:1009849400516 Zbl0937.47063
  5. [5] Chowdhury M.S.R., Generalized variational inequalities for upper hemi-continuous and demi operators with applications to fixed point theorems in Hilbert spaces, Serdica Math. J., 1998, 24, 163–178 Zbl0941.47054
  6. [6] Chowdhury M.S.R., The surjectivity of upper-hemi-continuous and pseudo-monotone type II operators in reflexive Banach Spaces, Ganit, 2000, 20, 45–53 Zbl1063.47503
  7. [7] Fan K., A minimax inequality and applications, In: Shisha O. (Ed.), Inequalities III, 103–113, Academic Press, San Diego, 1972 
  8. [8] Kneser H., Sur un theórème fundamental de la théorie des jeux, C. R. Acad. Sci. Paris, 1952, 234, 2418–2420 Zbl0046.12201
  9. [9] Shih M.-H., Tan K.-K., Generalized quasivariational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl., 1985, 108, 333–343 http://dx.doi.org/10.1016/0022-247X(85)90029-0 
  10. [10] Shih M.-H., Tan K.-K., Generalized bi-quasi-variational inequalities, J. Math. Anal. Appl., 1989, 143, 66–85 http://dx.doi.org/10.1016/0022-247X(89)90029-2 
  11. [11] Takahashi W., Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan, 1976, 28, 168–181 http://dx.doi.org/10.2969/jmsj/02810168 Zbl0314.47032

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