Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions

We prove the unconditional well-posedness result for fifth order modified KdV type equations in $H^s(\mathbb{T})$ when $s\ge 3\mathrm{/}2$, which includes non-integrable cases. By the conservation laws, we also obtain the global well-posedness result when $s=2$, which also includes non-integrable cases. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses.