Exceptional Families of Elements for Variational Inequalities in Banach Spaces
- 87 Downloads
In keeping with very recent efforts to establish a useful concept of an exceptional family of elements for variational inequality problems rather than complementarity problems as in the past, we propose such a concept. It generalizes previous ones to multivalued variational inequalities in general normed spaces and allows us to obtain several existence results for variational inequalities corresponding to earlier ones for complementarity problems. Compared with the existing literature, we consider problems in more general spaces and under considerably weaker assumptions on the defining map.
KeywordsVariational inequalities complementarity problems quasimonotone maps exceptional families of elements
Unable to display preview. Download preview PDF.
- 10.ISAC, G., and LI, J. L., Exceptional Family of Elements and the Solvability of Complementarity Problems in Uniformly Smooth and Uniformly Convex Banach Spaces, Journal of the Zhejiang University of Science, Vol. 6A, pp. 1–9, 2005.Google Scholar
- 14.AUBIN, J. P., and EKELAND, I., Applied Nonlinear Analysis, John Wiley and Sons, New York, NY, 1984.Google Scholar