IDEAS home Printed from https://ideas.repec.org/p/mil/wpdepa/2002-10.html
   My bibliography  Save this paper

A characterization of Ck,1 functions

Author

Listed:
  • 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.

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
    as

    Download full text from publisher

    File URL: http://wp.demm.unimi.it/files/wp/2002/DEMM-2002_010wp.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mil:wpdepa:2002-10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: DEMM Working Papers (email available below). General contact details of provider: https://edirc.repec.org/data/damilit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.