  For locally compact Hausdorff spaces $X$ and $Y$, and function algebras $A$
and $B$ on $X$ and $Y$, respectively, surjections $T:A \longrightarrow B$
satisfying norm multiplicative condition $\|Tf\, Tg\|_Y =\|fg\|_X$, $f,g\in A$,
with respect to the supremum norms, and those satisfying
$\||Tf|+|Tg|\|_Y=\||f|+|g|\|_X$ have been extensively studied. Motivated by
this, we consider certain (multiplicative or additive) subsemigroups $A$ and
$B$ of $C_0(X)$ and $C_0(Y)$, respectively, and study surjections $T: A
\longrightarrow B$ satisfying the norm condition $\rho(Tf, Tg)=\rho(f,g)$, $f,g
\in A$, for some class of two variable positive functions $\rho$. It is shown
that $T$ is also a composition in modulus map.
