Abstract
Let \(\cal L\)(X, Z) be the space of continuous linear mappings between topological vector spaces, where Z is Hausdorff and preordered by a closed convex cone C. In this paper, we introduce a notion of semicontinuity to any function from a topological space into X. A notion of semicontinuity is also introduced to any function from a topological space into \(\cal L\)(X, Z). These two notions of semicontinuity are related by the embedding of X into \(\cal L\)(X, Z). Their basic properties are given. As an application, we derive some existence results for the mixed vector variational-like inequality.
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Q.H. Ansari J.C. Yao (2001) ArticleTitleIterative-schemes for solving mixed variational-like inequalities Journal of Optimization Theory and Applications. 108 521–529 Occurrence Handle10.1023/A:1017531323904
Q.H. Ansari J.C. Yao (2000) ArticleTitleNonlinear variational inequalities for pseudomonotone operators with applications Advances in Nonlinear Variational Inequalities. 3 61–69
Q.H. Ansari J.C. Yao (1998) Prevariational inequalities in banach spaces L. Cacetta (Eds) Optimization Techniques and Applications Curtin University of Technology Perth, Australia 1165–1172
O. Chadli Y. Chiang S. Huang (2002) ArticleTitleTopological pseudomonotonicity and vector equilibrium problems Journal of Mathematical Analysis and Applications. 270 435–450 Occurrence Handle10.1016/S0022-247X(02)00079-3
G.Y. Chen (1989) ArticleTitleVector variational inequality and its applications for multiobjective optimization Chinese Science Bulletin. 34 969–972
G.Y. Chen X.Q. Yang (1990) ArticleTitleVector complementarity problem and its equivalence with weak minimal element in ordered spaces Journal of Mathematical Analysis and Applications 153 136–158 Occurrence Handle10.1016/0022-247X(90)90223-3
Chen G.Y., Cheng G.M. (1987). Vector variational inequalities and vector optimization. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, New York/Berlin, 285, 408-416.
G.Y. Chen S.L. Li (1996) ArticleTitleExistence of solutions for a generalized quasi-vector variational inequalities Journal of Optimization Theory and Applications. 90 321–334 Occurrence Handle10.1007/BF02190001
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This work was partially supported by grants from the National Science Council of the Republic of China.
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Chiang, Y. Semicontinuous Mappings into T.V.S. with Applications to Mixed Vector Variational-Like Inequalities. J Glob Optim 32, 467–484 (2005). https://doi.org/10.1007/s10898-003-2684-1
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DOI: https://doi.org/10.1007/s10898-003-2684-1