Question

explain plz..............

Answer 1

A functional is a real-valued function on a vector space , usually of functions. For example, the energy functional on the unit disk  assigns a number to any differentiable function ,



For the functional to be continuous, it is necessary for the vector space  of functions to have an appropriate topology. The widespread use of functionals in applications, such as the calculus of variations, gave rise to functional analysis.

The reason the term "functional" is used is because  can be a space of functions, e.g.,



in which case  is a linear functional on .