TOPICS
Search

Sublinear Function

A sublinear function on a real vector space is a function p satisfying positive homogeneity

p(alphax)=alphap(x)

for alpha>=0, and subadditivity

p(x+y)<=p(x)+p(y).

Every norm and every support function of a nonempty set is sublinear. A finite-valued function is sublinear iff it is both convex and positively homogeneous.

See also

Convex Function, Hahn-Banach Theorem, Norm

Explore with Wolfram|Alpha

References

Rockafellar, R. T. Convex Analysis. Princeton, NJ: Princeton University Press, 1970.

Cite this as:

Weisstein, Eric W. "Sublinear Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SublinearFunction.html

Subject classifications