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In this paper we study self-similar solutions in warped products satisfying $F-\mathcal{F}=\bar{g}(\lambda(r)\partial_{r},\nu)$, where $\mathcal{F}$ is a nonnegative constant and $F$ is in a class of general curvature functions including powers of mean curvature and Gauss curvature. We show that slices are the only closed strictly convex self-similar solutions in the hemisphere for such $F$. We also obtain a similar uniqueness result in hyperbolic space $\mathbb{H}^{3}$ for Gauss curvature $F$ and $\mathcal{F}\geq 1$.

self-similar solution, warped product