Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions
本文定义了隐式多值函数的正阶度量正则性与次正则性，利用Fréchet/Mordukhovich余导数给出了充分条件，并证明了在局部凸闭条件下这些条件也是必要的，进而建立了Hölder型性质和正阶平静性的判据。
We introduce concepts of metric regularity and metric subregularity of a positive-order for an implicit multifunction and provide new sufficient conditions for the implicit multifunctions to achieve the addressed properties. The conditions provided are presented in terms of the Fréchet/Mordukhovich coderivative of the corresponding parametric multifunction formulated the implicit multifunction. We show that such sufficient conditions are also necessary for the metric regularity/subregularity of a positive-order of the implicit multifunction when the corresponding parametric multifunction is (locally) convex and closed. In this way, we establish criteria ensuring that an implicit multifunction is Hölder-like and calm of a positive-order at a given point. As applications, we derive sufficient conditions in terms of coderivatives for a multifunction (resp., its inverse multifunction) to have the open covering property and the metric regularity/subregularity of a positive-order (resp., the Hölder-like/calm property).