Sharp bounds of logarithmic coefficients for a class of univalent functions

Let $\mathcal{U}(\mathcal{\alpha },\mathcal{\lambda })$, $0<\alpha <1$, $0<\lambda <1$ be the class of functions $f(z)=z+a_2{z}^2+a_3{z}^3+\cdots$ satisfying $$\mid {\left(\frac{z}{f(z)}\right)}^{1+\alpha }{f}^{\mathrm{\prime }}(z)-1\mid <\lambda$$ in the unit disc $\mathbb{D}$. For $f\in \mathcal{U}(\mathcal{\alpha },\mathcal{\lambda })$ we give sharp bounds of its initial logarithmic coefficients ${\gamma }_1,{\gamma }_2,{\gamma }_3\mathrm{.}$