Abstract
This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets. For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces, the authors prove some existence results of the solutions and the compactness of the solution sets. Especially, some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed. As applications, some existence theorems of the solutions of vector variational inequalities are obtained.
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This research was supported by the Science and Technology Foundation of Guizhou Province under Grant No. 20102133.
This paper was recommended for publication by Editor WANG Shouyang.
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Yu, J., Peng, D. Solvability of vector Ky Fan inequalities with applications. J Syst Sci Complex 26, 978–990 (2013). https://doi.org/10.1007/s11424-013-0284-9
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DOI: https://doi.org/10.1007/s11424-013-0284-9