Coefficient majorization conjecture for the class $cmathcal{B}_1(\alpha)$

Let $S$ denote the class of normalized univalent functions. For $0\leq\alpha\leq1$, suppose that $g\in S$ has the expansion $g(z)=z+b_2z^2+\cdots$ and satisfies

$$g'(z)\left[\frac{g(z)}{z}\right]^{\alpha-1}=1+2\sum_{n=1}^{\infty}z^n.$$

Let $f\in\mathcal{B}_1(\alpha)$ have the normalized expansion referred to as (A-05). Coefficient majorization conjecture. For every $n\geq2$,

$$|a_n|\leq b_n.$$

The paper presents this as an obvious conjecture in the coefficient problem for $\mathcal{B}_1(\alpha)$, extending known sharp estimates for low-order coefficients and the known $a_5$ bound in a restricted parameter range. Its resolution is not given in the supplied text.