  This note corrects a gap and improves results in an earlier paper by the
first named author.
  More precisely, it is shown that on weakly compactly generated Banach spaces
X which admit a C^{p} smooth norm, one can uniformly approximate uniformly
continuous functions f:X->R by Lipschitz, C^{p} smooth functions. Moreover,
there is a constant C>1 so that any L-Lipschitz function f:X->R can be
uniformly approximated by CL-Lipschitz, C^{p} smooth functions.
  This provides a `Lipschitz version' of the classical approximation results of
Godefroy, Troyanski, Whitfield and Zizler.
