Abstract
This paper is concerned with a generalized Ky Fan’s inequality. We first give an existence result of generalized Ky Fan’s (weak) efficient points, and then establish a complete metric space. Based on these results, we obtain the sufficient and necessary conditions of upper semicontinuity of efficient solution mapping to a generalized Ky Fan’s inequality. We also obtain the sufficient conditions of lower semicontinuity and continuity of efficient solution mapping to a generalized Ky Fan’s inequality. Our results are new and different from the corresponding ones in the literature.
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This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 11001287).
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Li, X.B., Wang, Q.L. & Peng, Z.Y. The stability of set of generalized Ky Fan’s points. Positivity 17, 501–513 (2013). https://doi.org/10.1007/s11117-012-0184-6
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DOI: https://doi.org/10.1007/s11117-012-0184-6