Uniform Continuity is Almost Lipschitz Continuity
Robert J. Vanderbei · 1997
We prove that uniformly continuous functions on convex sets are almost Lipschitz continuous in the sense that f is uniformly continuous if and only if, for every ǫ > 0, there exists a K < ∞, such that kf(y) − f(x)k ≤ Kky − xk + ǫ.