Abstract
In this paper, we introduce a class of generalized vector variational-like inequalities without monotonicity which generalizes and unifies generalized vector variational inequalities, vector variational inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence theorems for the generalized vector variational-like inequality without monotonicity are obtained in noncompact setting of topological vector spaces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubin J.P. and Ekeland I., “Applied Nonlinear Analysis”. J. Wiley and Sons, New York, 1984
Chen G.-Y., “Existence of solutions for a vector variational inequality: an extension of Hartman-Stampacchia Theorem”. Jou. Optim. Theory Appls., Vol. 74, 1992, pp. 445–456
Chen G.-Y. and Cheng G.M., “Vector Variational Inequalities and Vector Optimiz.”. Lecture Notes in Econ. and Mathem. System, No. 285, Springer-Verlag, Berlin, 1987, pp. 408–416
Chen G.-Y. and Craven B.D., “Approximate dual and approximate vector variational inequality for multiobjective optimization”. Jou. Austral. Mathem. Soc., ser. A, Vol 47, 1989, pp. 418–423.
Chen G.-Y. and Craven B.D., “A vector inequality and optimization over an efficient set”. Zeitschrift für Operations Research, Vol. 3, 1990, pp. 1–12.
Chen G.-Y. and Yang X.Q., “ The vector complementarity problem and its equivalences with the weak minial element in ordered spaces”. Jou. Mathem. Anal. Appls., Vol. 153, 1990, pp. 136–158.
Ding X.P. and Tan K.K., “Generalizations of KKM theorem and applications to best approximations and fixed point theorems”. SEA Bull. Mathem., Vol. 17 (2), 1993, pp. 139–150.
Giannessi F., “Theorems of the Alternative, Quadratic Programs, and Complementarity Problems.” In “Variational Inequalities and Complementarity Problems”, (Edited by R.W. Cottle, F. Giannessi and J.-L. Lions ), J. Wiley and Sons, New York, 1980, pp. 151–186.
Konnov I.V. and Yao J.C., “On the generalized vector variational inequality problem”. Jou. Mathem. Anal. Appls., Vol. 206, 1997, pp. 42–58.
Lai T.C. and Yao J.C., “Existence results for VVIP”. Appls. Mathem. Lett., Vol. 9 (3), 1996, pp. 17–19.
Lee G.M., Kim D.S. and Lee B.S., “Generalized vector variational inequality”, Appls. Mathem. Lett., Vol. 9 (1), 1996, pp. 39–42.
Lee G.M., Kim D.S. and Cho S.J., “ Generalized vector variational inequality and fuzzy extension”, Appls. Mathem. Lett., Vol. 6 (6), 1993, pp. 47–51.
Lin K.L., Yang D.P. and Yao J.C., “Generalized vector inequalities”. Jou. Optimiz. Theory Appls., Vol. 92 (1), 1997, pp. 117–125.
Parida I., Sahoo M. and Kumar A., “A variational-like inequality problem”. Bull. Austral. M.them. Soc., Vol. 39, 1989, pp. 225–231.
Schaefer H.H., “Topological Vector Spaces”. Springer-Verlag, New York, 1971.
Siddiqi A.H., Ansari Q.H. and Khaliq A., “On vector variational inequality”. Jou. Optimiz. Theory Appls., Vol. 84, 1995, pp. 171–180.
Yu S.J. and Yao J.C., “On vector variational inequalities”. Jou. Mathem. Anal. Appls., Vol. 89, 1996, pp. 749–769.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Kluwer Academic Publishers
About this chapter
Cite this chapter
Ding, X.P., Tarafdar, E. (2000). Generalized Vector Variational-Like Inequalities without Monotonicity. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0299-5_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7985-0
Online ISBN: 978-1-4613-0299-5
eBook Packages: Springer Book Archive