IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-1-4614-0619-8_2.html
   My bibliography  Save this book chapter

The Simplest Schemes of Generalized Solution of Linear Operator Equation

In: Generalized Solutions of Operator Equations and Extreme Elements

Author

Listed:
  • D. A. Klyushin

    (Kyiv National Taras Shevchenko University)

  • S. I. Lyashko

    (Kyiv National Taras Shevchenko University)

  • D. A. Nomirovskii

    (Kyiv National Taras Shevchenko University)

  • Yu. I. Petunin

    (Kyiv National Taras Shevchenko University)

  • V. V. Semenov

    (Kyiv National Taras Shevchenko University)

Abstract

The purpose of Chap. 2 is to give a natural definition of generalized solution of non-solvable linear operator equation in Banach spaces. In Sects. 2.1–2.4 two concepts of generalized solutions are proposed: strong generalized solution and weak generalized solution based on the duality. In Sect. 2.5 the theorem on existence of a weak generalized solution is proved. The relation between these two approaches is studied in Sect. 2.6 in the case of equations with linear injective operator.

Suggested Citation

  • D. A. Klyushin & S. I. Lyashko & D. A. Nomirovskii & Yu. I. Petunin & V. V. Semenov, 2012. "The Simplest Schemes of Generalized Solution of Linear Operator Equation," Springer Optimization and Its Applications, in: Generalized Solutions of Operator Equations and Extreme Elements, edition 1, chapter 0, pages 7-15, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0619-8_2
    DOI: 10.1007/978-1-4614-0619-8_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spochp:978-1-4614-0619-8_2. 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: 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.