- A SHARP SCHWARZ LEMMA AT THE BOUNDARY
- AKYEL, TUGBA ; ORNEK, NAFI ;
- The Pure and Applied Mathematics, volume 22, issue 3, 2015, Pages 263~273
- DOI : 10.7468/jksmeb.2015.22.3.263

Abstract

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + c_{p}z^{p} + c_{p}+_{1}z^{p+1} + ... defined in the unit disc satisfying |f(z) − 1| < 1, where 0 < a < 2, we estimate a module of angular derivative at the boundary point b, f(b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.