IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-662-00547-7_9.html
   My bibliography  Save this book chapter

Extremal Problems

In: Nonlinear Functional Analysis

Author

Listed:
  • Klaus Deimling

    (Gesamthochschule Paderborn)

Abstract

The common denominator of the three parts forming this chapter is the search for extrema of real-valued functionals φ over various subsets Ω of usually infinite-dimensional Banach spaces X under various conditions on φ, Ω and X. The need for an abstract ordering of ideas concerning the minimization of certain functions on ‘collections of functions’ (the calculus of variations) is one of the origins of what is called functional analysis today, but not the only one, as you are led to believe in some books on the variational calculus. For the history of the latter you may consult Goldstine [1] and some remarks in Young [1]. If you are interested in the history of functional analysis, you should not miss the booklet of F. Riesz [1] or the recent retrospection of Dieudonné [2], the fourth chapter of which draws from the work of Riesz — to mention just two references. These days optimization theory is no doubt the most popular mathematical discipline for the ‘users’ (besides probability theory), if the incredible flood of books on the subject is a measure of popularity (‘that’s what sells’). So it may be useful to have an abstract of the abstraction, showing in particular how some techniques from other chapters may be used here.

Suggested Citation

  • Klaus Deimling, 1985. "Extremal Problems," Springer Books, in: Nonlinear Functional Analysis, chapter 0, pages 319-377, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-00547-7_9
    DOI: 10.1007/978-3-662-00547-7_9
    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
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-662-00547-7_9. 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.