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A characterization of Ck,1 functions

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  • Davide La Torre

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  • Matteo Rocca

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Abstract

In this work we provide a characterization of C{k,1} functions on Rn (that is k times differentiable with locally Lipschitzian k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of C{k,1} functions is equivalent to the class of functions with bounded (k+1)-th divided difference. From this result we deduce aTaylor's formula for this class of functions and a characterization through Riemann derivatives.

Suggested Citation

  • Davide La Torre & Matteo Rocca, 2002. "A characterization of Ck,1 functions," Departmental Working Papers 2002-10, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2002-10
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    Cited by:

    1. Davide La Torre & Carlo Vercellis, 2002. "C1,1 approximations of generalized support vector machines," Departmental Working Papers 2002-19, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2002. "C 1,1 vector optimization problems and Riemann derivatives," Economics and Quantitative Methods qf0210, Department of Economics, University of Insubria.
    3. Davide La Torre & Matteo Rocca, 2002. "A survey on C1,1 functions: Theory, numerical methods and applications," Departmental Working Papers 2002-12, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    4. Davide LaTorre, 2002. "On generalized derivatives for C1,1 vector functions and optimality conditions," Departmental Working Papers 2002-20, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Davide La Torre & Giovanni Crespi & Matteo Rocca, 2002. "Second order optimality conditions for differentiable functions," Departmental Working Papers 2002-02, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    6. La Torre Davide & Rocca Matteo, 2002. "C 1,1 functions and optimality conditions," Economics and Quantitative Methods qf0208, Department of Economics, University of Insubria.
    7. Matteo Fini, 2003. "Uno sguardo sul concetto di differenziale dalle origini ai giorni nostri: tra storia e teoria," Departmental Working Papers 2003-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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