Conjecture on consecutive logarithmic coefficients of univalent functions

Let $f\in\mathcal{S}$ be a univalent function with logarithmic coefficients $\gamma_n$, defined by the logarithmic expansion associated with $f$. Conjecture on consecutive logarithmic coefficients. For every integer $n\geq 3$, one has

$$|\gamma_n|-|\gamma_{n-1}|\leq \frac{1}{\sqrt{2n-1}}.$$

The preceding theorem establishes the corresponding estimate for $n=3$; the assertion for all $n\geq 4$ remains open in the supplied text.