A sublinear function on a real vector space is a real-valued function 
satisfying positive homogeneity
for 
,
and subadditivity
Every norm and every convex body support function of a nonempty convex
body is sublinear. A finite-valued function is sublinear
iff it is both convex
and positively homogeneous.
See also
Convex Function,
Hahn-Banach
Theorem,
Norm
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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
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