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Hölder Continuity of the Solution Set of the Ky Fan Inequality

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Abstract

This paper is concerned with the Hölder continuity of the perturbed solution set to a convex Ky Fan Inequality. We establish some new sufficient conditions for the uniqueness and Hölder continuity of the solution set of the Ky Fan Inequality both in the given space and in its image space by perturbing the objective function and the feasible set. Our methods and results are different from the corresponding ones in the literature. Some examples are given to analyze the obtained results.

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Acknowledgements

The authors would like to express their deep gratitude to the anonymous referees for their valuable comments and suggestions, which helped to improve the paper.

This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 11201509, 11001287 and 11271389) and the Natural Science Foundation Project of CQ CSTC (Grant numbers: cstc2012jjA00016 and cstc2012jjA00038).

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Authors and Affiliations

  1. College of Sciences, Chongqing Jiaotong University, Chongqing, 400074, China

    X. B. Li

  2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    X. J. Long & J. Zeng

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  1. X. B. Li
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  2. X. J. Long
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  3. J. Zeng
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Correspondence to X. B. Li.

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Li, X.B., Long, X.J. & Zeng, J. Hölder Continuity of the Solution Set of the Ky Fan Inequality. J Optim Theory Appl 158, 397–409 (2013). https://doi.org/10.1007/s10957-012-0249-5

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