First of all, notice that $r_0$ must be $2^*$ instead of $2^*-q$. Indeed, from page 160 of the paper one has that $q\in(1, 2^*)$ and from the beginning of the proof of the theorem 2.1 (page 162 in step 1), one has that $\gamma +2<q<\text{max}(p,2^*)$, which implies that $q\in (2, 2^*)$. Then, if $r_0=2^*-q$ and $r_1=\frac{2^*}{2}r_0+\frac{2^*}{2}(2-q)$ then $\left(\frac{2^*}{2}\right)(r_0+2-q)> (r_0+2-q)$ since $\left(\frac{2^*}{2}\right)>1$. However, $(r_0+2-q)>r_0 \iff 2-q> 0\iff q<2$. Contradicting the fact that $q\in (2, 2^*)$.
Now, let'sLet's see the iteration
