fixedpoint theorem
fixedpoint theorem A theorem concerning the existence and nature of fixed points used to give solutions to equations. A fixed point of a function f f : X → X
is an element x such that f(x) = x. A least fixed point is one that, among all the fixed points of f, is lowest in some partial ordering that has been imposed on the elements of X. Specifically, if ← is a partial ordering of X then x is a least fixed point if for fixed point y we have x ← y.
The most oftencited form of fixedpoint theorem to do with computing is due originally to S. C. Kleene, and originated in recursive function theory. It states that, subject to certain assumptions, notably that f is continuous, f has a least fixed point, x_{f}, which moreover can be characterized as the limit of a sequence x_{0},x_{1},x_{2},… of approximations. This abstract fact is of great relevance to the semantics of programming languages, in particular in specifying the precise meaning of constructs like iteration, recursion, and recursive types using equations.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"fixedpoint theorem." A Dictionary of Computing. . Encyclopedia.com. 16 Aug. 2018 <http://www.encyclopedia.com>.
"fixedpoint theorem." A Dictionary of Computing. . Encyclopedia.com. (August 16, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/fixedpointtheorem
"fixedpoint theorem." A Dictionary of Computing. . Retrieved August 16, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/fixedpointtheorem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.