Some equivalence relations between some best approximationsand some best approximate elements in the Besov space

This paper establishes some equivalence relations between some best approximations and some best approximate elements in various Besov spaces.Theorem 1 is an essential extension of Theorem 4.2 of the paper of Cohen, et al(2000) and Theorem 2 extends Theorem 7 of the paper of Li Song(1997) to the case 0p≤∞.