An analytic function $f$ defined on the open unit disk is biunivalent if the function $f$ and its inverse ${f}^{-1}$ are univalent in $\mathbb{D}$. Estimates for the initial coefficients of biunivalent functions $f$ are investigated when $f$ and ${f}^{-1}$, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

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