On the moduli of convexity

It is known that, given a Banach space , the modulus of convexity associated to this space is a non-negative function, non-decreasing, bounded above by the modulus of convexity of any Hilbert space and satisfies the equation for every , where is a constant. We show that, given a function satisfying these properties then, there exists a Banach space in such a way its modulus of convexity is equivalent to , in Figiel's sense. Moreover this Banach space can be taken to be two-dimensional.