Some remarks for a certain class of holomorphic functions at the boundary of the unit disc

We consider a boundary version of the Schwarz Lemma on a certain class which is denoted by ?(?). For the function ?(?) = ? + ???? + ????+. .. which is defined in the unit disc ? such that the function ?(?) belongs to the class ?(?), we estimate from below the modulus of the angular derivative of the function ??'(?) ?(?) at the boundary point ? with ??'(?) ?(?) = ? ??? . Moreover, we get the Schwarz Lemma for the class ?(?). We also investigate some inequalities obtained in terms of sharpness.

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