A special case of a non-linear operator defined on a real (or complex) vector space $X$ and whose values are real (or complex) numbers. Examples of non-linear functionals are the functionals of the calculus of variations,
or convex functionals, defined by the condition
$$f(\lambda y+(1-\lambda)x)\leq\lambda f(y)+(1-\lambda)f(x),$$
where $x,y\in X$, $0\leq\lambda\leq1$, and, say, $f(x)=\|x\|$ — the norm of an element in a normed space.
See also Non-linear functional analysis.
Non-linear functional. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-linear_functional&oldid=33290