Implicit Multifunction Theorems

Ledyaev, Yuri S. and Zhu, Qiji J. (1998) Implicit Multifunction Theorems. [Preprint]

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      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.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: nonsmooth analysis, subdifferentials, coderivatives, implicit function theorem, solvability, stability, open mapping theorem, metric regularity, multidirectional mean value inequality
      Subjects: 26-xx Real functions > 26Bxx Functions of several variables
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 21 Apr 2010 11:13

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