Multivalued function

An example of a multifunction: the input 3 is associated with both the output b and the output c.

A multivalued function (multifunction) is a relation like a function. A multifunction associates each input with at least one output. A strict function associates each input with exactly one output. An example of a multivalued function is the square root. Every complex number (except for 0), has two square roots. Example: ${\sqrt {4}}$ could be 2 or -2 because $2^{2}=4$ and $(-2)^{2}=4$.

References

• Flavia-Corina Mitroi-Symeonidis, A sandwich theorem for convex set-valued functions, An. Univ. Oradea fasc. mat., vol. 23, issue 1 (2016), pp. 77-79. ISSN: 1221-1265.

• Flavia-Corina Mitroi, Kazimierz Nikodem, Szymon Wąsowicz, Hermite-Hadamard inequalities for convex set-valued functions, Demonstratio Mathematica, Vol. 46, Issue 4(2013), pp.655-662. ISSN: 0420-1213.