Implicit Multifunction Theorems |
| |
Authors: | Yuri S. Ledyaev and Qiji J. Zhu |
| |
Affiliation: | (1) Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI, 49008, U.S.A. |
| |
Abstract: | We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest. |
| |
Keywords: | nonsmooth analysis subdifferentials coderivatives implicit function theorem solvability stability open mapping theorem metric regularity multidirectional mean value inequality |
本文献已被 SpringerLink 等数据库收录! |