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DOI: 10.23952/cot.2023.33
Received December 30, 2022; Accepted February 26, 2023; Published July 7, 2023
Abstract. In this paper, by introducing a key assumption, we discuss the Hölder-likeness and the q-order metric regularity of an implicit multifunction. Firstly, 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 Hölder-likeness (metric regularity) of the implicit multifunction. Then, by the Robinson metric regularity we establish the contingent derivative and the second-order contingent derivative for the implicit multifunction. Finally, we apply the results obtained to the solution mapping of a parametric vector equilibrium problem.
How to Cite this Article:
C.M. Liao, M.H. Li, X.W. Xue, Hölder-likeness and first (second)-order contingent derivatives of an implicit multifunction, Commun. Optim. Theory 2023 (2023) 33.