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A characterization of Ck,1 functions

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  • Davide La Torre

    ()

  • Matteo Rocca

    ()

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.

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Bibliographic Info

Paper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2002-10.

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Date of creation: 01 Jan 2002
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Handle: RePEc:mil:wpdepa:2002-10

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Cited by:
  1. 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.
  2. La Torre Davide & Rocca Matteo, 2002. "C 1,1 functions and optimality conditions," Economics and Quantitative Methods qf0208, Department of Economics, University of Insubria.
  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. 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.
  5. La Torre Davide & Rocca Matteo, 2002. "A survey on C 1,1 fuctions: theory, numerical methods and applications," Economics and Quantitative Methods qf0207, Department of Economics, University of Insubria.
  6. 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.
  7. Davide La Torre & Matteo Rocca, 2002. "C1,1 functions and optimality conditions," Departmental Working Papers 2002-13, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  8. 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.
  9. 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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