Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (1): 17-23.doi: 10.3969/j.issn.1000-5641.2018.01.003

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Lipschitz-likeness and contingent derivative of an implicit multifunction

WANG Li-na1, FANG Zhi-miao2, LI Ming-hua3   

  1. 1. Chongqing Water Resources and Electric Engineering College, Chongqing 402160, China;
    2. Department of Basic Courses, Chongqing Police College, Chongqing 401331, China;
    3. College of Mathematics and Finance, Chongqing University of Arts and Sciences Chongqing 402160, China
  • Received:2016-12-21 Online:2018-01-25 Published:2018-01-11

Abstract: In this paper by introducing a key assumption, we prove that the key assumption is equivalent to the Robinson metric regularity of the implicit multifunction and that under some suitable conditions the key assumption is sufficient for the Lipschitz-likeness (metric regularity) of the implicit multifunction. Finally, we establish the specific expressions of the contingent derivative and the second-order contingent derivative for the implicit multifunction.

Key words: implictit multifunction, Robinson metric regularity, Lipschitz-likeness, contingent derivative

CLC Number: