Lipschitz continuity

In mathematics, a function

Hölder continuity

If a map f: M → N satisfies the Lipschitz-like condition

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:d(f(x), f(y)) ≤ Kd(x, y)α

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

for some α > 0 (the order) and all x, y, it is said to be Hölder-continuous or α-Hölder.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~