isomorphisms in unital $c^*$-algebras

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when  $h(3^n u y) =h(3^n u) h(y)$  for all  $u in { v in a mid v = v^*, |v|=1, v text{ is invertible} }$, all$y in a$, and all $nin mathbb z$.assume that $x$ and $y$  are left normed modules over a unital$c^*$-algebra $a$. it is shown that every surjective isometry $t : xrightarrow y$, satisfying $t(0) =0$ and $t(ux) = u t(x)$ for all $xin x$ and all unitaries $u in a$, is an $a$-linear isomorphism.this is applied to investigate $c^*$-algebra isomorphisms in unital$c^*$-algebras.