Loterre: Mathematics: sublinear function

mathematical analysis > functional analysis > sublinear function

mathematical analysis > function > sublinear function

geometry > convex analysis > sublinear function

algebra > linear algebra > linear map > sublinear function

sublinear function

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional, on a vector space ${\\displaystyle X}$ is a real-valued function with only some of the properties of a seminorm. Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known notion of norms, where a seminorm has all the defining properties of a norm except that it is not required to map non-zero vectors to non-zero values.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Sublinear_function)

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