A function f: X -> Y is Hölder continuous if and only if there exists a constant K > 0 and α ∈ (0,1] such that d_Y(f(x),f(y)) ≤ Kd_X(x,y)^α for all x,y in X.
A function f: X -> Y is Hölder continuous if and only if there exists a constant K > 0 and α ∈ (0,1] such that d_Y(f(x),f(y)) ≤ Kd_X(x,y)^α for all x,y in X.