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Let ${\mathcal A}$ be the class of functions $f$ that are analytic in theunit disk ${\mathbb D}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$.Let $0<\lambda\le1$ and \[ {\mathcal U}(\lambda) = \left\{ f\in{\mathcal A}:\left |\left (\frac{z}{f(z)} \right )^{2}f'(z)-1\right | < \lambda,\,z\in{\mathbb D} \right\}. \] In this paper sharp upper bounds of the firstthree coefficients of the inverse function $f^{-1}$ are given in the case when\[\frac{f(z)}{z}\prec \frac{1}{(1-z)(1-\lambda z)}.\]

Coefficients of the inverse of functions for the subclass of $\mathcal U (\lambda)$