Set-valued function

For multi-valued functions of mathematical analysis, see Multivalued function. For functions whose arguments are sets, see Set function.
This diagram represents a multi-valued, but not a proper (single-valued) function, because the element 3 in X is associated with two elements, b and c, in Y.

A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set.[1][2] Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory.

Set-valued functions are also known as multivalued functions in some references,[3] but this article and the article Multivalued function follow the authors who make a distinction.

  1. ^ Aliprantis, Charalambos D.; Border, Kim C. (2013-03-14). Infinite Dimensional Analysis: A Hitchhiker's Guide. Springer Science & Business Media. p. 523. ISBN 978-3-662-03961-8.
  2. ^ Wriggers, Peter; Panatiotopoulos, Panagiotis (2014-05-04). New Developments in Contact Problems. Springer. p. 29. ISBN 978-3-7091-2496-3.
  3. ^ Repovš, Dušan (1998). Continuous selections of multivalued mappings. Pavel Vladimirovič. Semenov. Dordrecht: Kluwer Academic. ISBN 0-7923-5277-7. OCLC 39739641.