Real Analysis Exchange

C1 selections of multifunctions in one dimension

Craig Knuckles and Peter R. Wolenski

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Sufficient conditions are given for a multifunction (set-valued function) to admit a continuously differentiable selection in one dimension. These conditions are given in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction.

Article information

Real Anal. Exchange, Volume 22, Number 2 (1996), 655-676.

First available in Project Euclid: 22 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26E25: Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]

smooth selection Lipschitz multifunction submonotone Multifunction subdifferentially regular function semismooth function


Knuckles, Craig; Wolenski, Peter R. C 1 selections of multifunctions in one dimension. Real Anal. Exchange 22 (1996), no. 2, 655--676.

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