Volume 3, Issue 3-1, June 2015, Page: 46-53
Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets
Mohammad S. R. Chowdhury, Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Yeol Je Cho, Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Korea; Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
Received: Apr. 5, 2015;       Accepted: Apr. 9, 2015;       Published: Jun. 17, 2015
DOI: 10.11648/j.ajam.s.2015030301.18      View  3407      Downloads  65
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.
Generalized Quasi-Variational Inequalities, Pseudo-Monotone Type III Operators, Locally Convex Topological Vector Spaces
To cite this article
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, American Journal of Applied Mathematics. Special Issue: Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015). Vol. 3, No. 3-1, 2015, pp. 46-53. doi: 10.11648/j.ajam.s.2015030301.18
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.
K. Fan, A minimax inequality and applications, in “Inequalities, III” (O. Shisha, Ed.), pp.103-113, Academic Press, San Diego, 1972.
D. Chan and J. S. Pang, The generalized quasi-variational inequality problem, Math. Oper. Res. 7(1982), 211-222.
M.-H. Shih and K.-K. Tan, Generalized quasivariational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl., 108 (1985), 333-343.
Mohammad S. R. Chowdhury and E. Tarafdar, Hemi-continuous operators and some applications, Acta Math. Hungar. 83(3) (1999), 251-261.
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.
W. Takahashi, Nonlinear variational inequalities and fixed point theorems, Journal of the Mathematical Society of Japan, 28 (1976), 168-181.
M.-H. Shih and K.-K. Tan, Generalized bi-quasi-variational inequalities, J. Math. Anal. Appl., 143 (1989), 66-85.
H. Kneser, Sur un théorème fondamental de la théorie des jeux, C. R. Acad. Sci. Paris, 234 (1952), 2418-2420.
J. P. Aubin, Applied Functional Analysis, Wiley-Interscience, New York, 1979.
J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
R. T. Rockafeller, Convex Analysis, Princeton Univ., Princeton, 1970.
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.
Browse journals by subject