We first define upper sign continuity for a set-valued mapping
and then we consider two types of generalized vector equilibrium problems in topological
vector spaces and provide sufficient conditions under which the solution sets are nonempty
and compact. Finally, we give an application of our main results. The paper generalizes
and improves results obtained by Fang and Huang in (2005).
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References
Y.-P. Fang and N.-J. Huang, ``Existence results for generalized implicit vector variational inequalities with multivalued mappings,'' Indian Journal of Pure and Applied Mathematics, vol. 36, no. 11, pp. 629--640, 2005.
N. T. Tan, ``Quasi-variational inequalities in topological linear locally convex Hausdorff spaces,'' Mathematische Nachrichten, vol. 122, no. 1, pp. 231--245, 1985.
Mathematical Reviews (MathSciNet):
MR871206
M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, vol. 7 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 2001.
M. Bianchi and R. Pini, ``Coercivity conditions for equilibrium problems,'' Journal of Optimization Theory and Applications, vol. 124, no. 1, pp. 79--92, 2005.
N. Hadjisavvas, ``Continuity and maximality properties of pseudomonotone operators,'' Journal of Convex Analysis, vol. 10, no. 2, pp. 465--475, 2003.
H. Yin and C. Xu, ``Vector variational inequality and implicit vector complementarity problems,'' in Vector Variational Inequalities and Vector Equilibria, F. Giannessi, Ed., vol. 38 of Nonconvex Optimization and Its Applications, pp. 491--505, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
K. Fan, ``Some properties of convex sets related to fixed point theorems,'' Mathematische Annalen, vol. 266, no. 4, pp. 519--537, 1984.
Mathematical Reviews (MathSciNet):
MR735533
S. Park, ``Recent results in analytical fixed point theory,'' Nonlinear Analysis: Theory, Methods & Applications, vol. 63, no. 5--7, pp. 977--986, 2005. \endthebibliography
