Publications de l’Institut Mathématique, Nouvelle Série, Vol. 101[115], pp. 191

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 101[115], pp. 191–196 (2017)

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REPRESENTATION WITH MAJORANT OF THE SCHWARZ LEMMA AT THE BOUNDARY

Bülent Nafi Örnek, Tuğba Akyel

Department of Mathematics, Gebze Technical University, Gebze-Kocaeli, Turkey

Abstract: Let $f$ be a holomorphic function in the unit disc $D$ and $| f (z) - 1 | < 1$ for $| z | < 1$ . We generalize a uniqueness portion of Schwarz’s lemma and provide sufficient conditions on the local behavior of $f$ near a finite set of boundary points that needs $f$ to be a finite Blaschke product.

Keywords: Schwarz lemma; Holomorphic function; Blaschke product; Hopf’s lemma on the disc

Classification (MSC2000): 30C80; 32A10

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Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.

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