摘要
For continuous vector-valued functions, we discuss relations among exponential and polynomial growth orders of the γ-Cesàro mean (γ ≥ 0) and of the Abel mean. In general, the Abel mean has growth order not larger than those of Cesáro means, and a higher-order Cesáro mean has a smaller growth order than a lower-order Cesáro mean. But, for a positive function in a Banach lattice, the Abel mean and all γ-Cesáro means with γ ≥ 1 (but not with 0 ≤ γ< 1) have the same polynomial growth order. The possibility of non-equal growth orders for these means is illustrated by some examples of C <sub>0</sub> -semigroups and cosine operator functions.