Let $(X,d)$ be a real metric linear space, 
with translation-invariant metric $d$ and $G$ 
a linear subspace of $X$. In this paper we use 
functionals in the Lipschitz dual of $X$ to 
characterize those elements of $G$ which are 
best approximations to elements of $X$.

We also give simultaneous characterization of 
elements of best approximation and also 
consider elements of $\epsilon$-approximation.