Interpolation methods for multivalued functions

Abstract

The notion of multivalued functions appeared in the first half of the twentieth century. A multivalued function also known as multi-function, multimap, set-valued function. This is a ”function” that assume two or more values for each point from the domain. These functions are not functions in the classical way because for each point assign a set of points, so there is not a one-to-one correspondence. The term of ”multivalued function” is not correct, but became very popular. Multivalued functions often arise as inverse of functions which are not-injective. For example the inverse of the trigonometric, exponential, power or hyperbolic functions are multivalued functions. Also the indefinite integral can be considered as a multivalued function. These functions appears in many areas, for example in physics in the theory of defects of crystals, for vortices in superfluids and superconductors but also in optimal control theory or game theory in mathematics.