Sharp bounds of logarithmic coefficients for a class of univalent functions

Abstract

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