A class of curvature flows expanded by support function and curvature function

In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean mathbb{R}^{n+1} with speed u^alpha f^beta (alpha, betainmathbb{R}^1), where u is support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If alpha leq 0<betaleq 1-alpha, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin.