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At each time $n\in\mathbb{N}$, let$\bar{Y}^{(n)}=(y_{1}^{(n)},y_{2}^{(n)},\cdots)$ be a random sequence ofnon-negative numbers that are ultimately zero in a random environment$\xi=(\xi_{n})_{n\in\mathbb{N}}$ in time, which satisfies for each$n\in\mathbb{N}$ and a.e.$\xi,~E_{\xi}[\sum_{i\in\mathbb{N}_{+}}y_{i}^{(n)}(\xi)]=1.$ The existence anduniqueness of the non-negative fixed points of the associated smoothingtransform in random environments is considered. These fixed points aresolutions of the distributional equation for$a.e.~\xi,~Z(\xi)\overset{d}{=}\sum_{i\in\mathbb{N}_{+}}y_{i}^{(0)}(\xi)Z_{i}(T\xi),$where when given the environment $\xi$, $Z_{i}(T\xi)~(i\in\mathbb{N}_{+})$ 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 inrandom environments is given as well. The classical results by Biggins (1977)has been extended to the random environment situation.

Fixed points with finite mean of the smoothing transform in random environments