  In this erratum, we recover the results from an earlier paper of the author's
which contained a gap. Specifically, we prove that if X is a Banach space with
an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and
Y is a convex subset of X, then any uniformly continuous function f: Y->R can
be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if
Z is any Banach space and f:X->Z is L-Lipschitz, then the approximates K:X->Z
can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only
on X.
