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

• Autorzy: Mohammad Chowdhury , Kok-Keong Tan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Generalized bi-quasi-variational inequalities; Quasi-pseudomonotone type II operators; Strongly quasi-pseudo-monotone type II operators; Locally convex Hausdorff topological vector spaces

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H04: Set-valued operators
• 54C60: Set-valued maps
• 49J35: Minimax problems
• 47H10: Fixed-point theorems
• 49J40: Variational methods including variational inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 158-169

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Mohammad Chowdhury

• Lahore University of Management Sciences (LUMS)

autor

Kok-Keong Tan

• Dalhousie University

Bibliografia

• [1] Aubin J.P., Applied Functional Analysis, Wiley-Interscience, New York, 1979
• [2] Brézis H., Nirenberg L., Stampacchia G., A remark on Ky Fan’s minimax principle, Boll. Un. Mat. Ital. (4), 1972, 6, 293–300
• [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] 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
• [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
• [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
• [7] Fan K., A minimax inequality and applications, In: Shisha O. (Ed.), Inequalities III, 103–113, Academic Press, San Diego, 1972
• [8] Kneser H., Sur un theórème fundamental de la théorie des jeux, C. R. Acad. Sci. Paris, 1952, 234, 2418–2420
• [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] 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] 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

Identyfikatory

DOI

10.2478/s11533-009-0066-8