At each time $ninmathbb{N}$, let $bar{Y}^{(n)}=(y_{1}^{(n)},y_{2}^{(n)},cdots)$ be a random sequence of non-negative numbers that are ultimately zero in a random environment $xi=(xi_{n})_{ninmathbb{N}}$ in time, which satisfies for each $ninmathbb{N}$ and a.e. $xi,~E_{xi}[sum_{iinmathbb{N}_{+}}y_{i}^{(n)}(xi)]=1.$ The existence and uniqueness of the non-negative fixed points of the associated smoothing transform in random environments is considered. These fixed points are solutions of the distributional equation for $a.e.~xi,~Z(xi)overset{d}{=}sum_{iinmathbb{N}_{+}}y_{i}^{(0)}(xi)Z_{i}(Txi),$ where when given the environment $xi$, $Z_{i}(Txi)~(iinmathbb{N}_{+})$ are $i.i.d.$ non-negative random variables, and distributed the same as $Z(xi)$. As an application, the martingale convergence of the branching random walk in random environments is given as well. The classical results by Biggins (1977) has been extended to the random environment situation.
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