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A characterization of Ck,1 functions

Author

Listed:
  • La Torre Davide

    (Department of Economics,University of Milan, Italy)

  • Rocca Matteo

    (Department of Economics, University of Insubria, Italy)

Abstract

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

Suggested Citation

  • La Torre Davide & Rocca Matteo, "undated". "A characterization of Ck,1 functions," Economics and Quantitative Methods qf0103, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0103
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    Cited by:

    1. La Torre Davide & Rocca Matteo, 2002. "C 1,1 functions and optimality conditions," Economics and Quantitative Methods qf0208, Department of Economics, University of Insubria.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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