Set-valued function
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, 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. 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, but this article and the article Multivalued function follow the authors who make a distinction.
, 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. 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, but this article and the article Multivalued function follow the authors who make a distinction. The argmax of a function is in general, multivalued. For example, \operatorname{argmax}_{x \in \mathbb{R}} \cos(x) = \{2 \pi k\mid k \in \mathbb{Z}\} . K. Deimling, Multivalued Differential Equations, Walter de Gruyter, 1992 C. D. Aliprantis and K. C. Border, Infinite dimensional analysis. Hitchhiker's guide, Springer-Verlag Berlin Heidelberg, 2006 J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, 2003 J.-P. Aubin and A. Cellina, Differential Inclusions, Set-Valued Maps And Viability Theory, Grundl. der Math. Wiss. 264, Springer - Verlag, Berlin, 1984 J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Basel, 1990 D. Repovš and P.V. Semenov, Continuous Selections of Multivalued Mappings, Kluwer Academic Publishers, Dordrecht 1998 E. U. Tarafdar and M. S. R. Chowdhury, Topological methods for set-valued nonlinear analysis, World Scientific, Singapore, 2008
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