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Openness results for parametric set-valued mappings in Asplund spaces

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Abstract

In this paper, we first prove a lemma about the lower semicontinuity of the distance function in infinite dimensional spaces, which is crucial to openness results hereafter. Then we obtain some openness results in terms of Fréchet coderivatives for parametric set-valued mappings in Asplund spaces under mild conditions. The results of the paper generalize several corresponding results in the recent literature. Finally, we give two examples to illustrate our openness results.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (No. 11226228, 11201214, 11301254), the Science and Technology Program Project of Henan Province of China (No. 122300410256) and the Natural Science Foundation of Henan Education Department of China (No. 2011B110025).

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Authors and Affiliations

  1. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, Henan, People’s Republic of China

    Ming-ge Yang

  2. School of Management, Fudan University, Shanghai, 200433, People’s Republic of China

    Ming-ge Yang & Yi-fan Xu

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  1. Ming-ge Yang
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  2. Yi-fan Xu
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Correspondence to Ming-ge Yang.

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Yang, Mg., Xu, Yf. Openness results for parametric set-valued mappings in Asplund spaces. Optim Lett 8, 2227–2243 (2014). https://doi.org/10.1007/s11590-014-0730-1

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  • DOI: https://doi.org/10.1007/s11590-014-0730-1

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