IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v147y2010i3d10.1007_s10957-010-9730-1.html
   My bibliography  Save this article

The Hahn Quantum Variational Calculus

Author

Listed:
  • A. B. Malinowska

    (Białystok University of Technology)

  • D. F. M. Torres

    (University of Aveiro)

Abstract

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann’s direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.

Suggested Citation

  • A. B. Malinowska & D. F. M. Torres, 2010. "The Hahn Quantum Variational Calculus," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 419-442, December.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9730-1
    DOI: 10.1007/s10957-010-9730-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9730-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9730-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. A. Carlson & G. Leitmann, 2005. "Coordinate Transformation Method for the Extremization of Multiple Integrals," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 523-533, December.
    2. F. O. O. Wagener, 2009. "On the Leitmann Equivalent Problem Approach," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 229-242, July.
    3. D.A. Carlson, 2002. "An Observation on Two Methods of Obtaining Solutions to Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 345-361, August.
    4. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    5. D. F. M. Torres & G. Leitmann, 2008. "Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 53-59, April.
    6. Dean A. Carlson & George Leitmann, 2005. "A Direct Method for Open-Loop Dynamic Games for Affine Control Systems," Springer Books, in: Alain Haurie & Georges Zaccour (ed.), Dynamic Games: Theory and Applications, chapter 0, pages 37-55, Springer.
    7. G. Leitmann, 2001. "Some Extensions to a Direct Optimization Method," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 1-6, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. M. H. Annaby & A. E. Hamza & K. A. Aldwoah, 2012. "Hahn Difference Operator and Associated Jackson–Nörlund Integrals," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 133-153, July.
    2. Nichaphat Patanarapeelert & Thanin Sitthiwirattham, 2019. "On Fractional Symmetric Hahn Calculus," Mathematics, MDPI, vol. 7(10), pages 1-18, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. D. F. M. Torres & G. Leitmann, 2008. "Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 53-59, April.
    2. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    3. Florian Wagener, 2025. "On the infinite horizon linear-quadratic regulator problem and the Leitmann transformation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 345-349, June.
    4. D. A. Carlson & G. Leitmann, 2004. "An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 27-47, October.
    5. F. O. O. Wagener, 2009. "On the Leitmann Equivalent Problem Approach," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 229-242, July.
    6. S. G. Ji & S. Y. Shi, 2006. "Periodic Solutions for a Class of Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 125-137, July.
    7. D.A. Carlson, 2002. "An Observation on Two Methods of Obtaining Solutions to Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 345-361, August.

    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:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9730-1. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.