Open AccessOn the Schwarz lemma at the upper half plane
Author(s) -
Bülent Örnek Nafi
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1910995o
Subject(s) - mathematics , holomorphic function , boundary (topology) , lemma (botany) , plane (geometry) , mathematical analysis , upper and lower bounds , complex plane , upper half plane , function (biology) , combinatorics , pure mathematics , geometry , ecology , poaceae , evolutionary biology , biology
In this paper, we give a simple proof for the boundary Schwarz lemma at the upper half plane. Considering that f(z) is a holomorphic function defined on the upper half plane, we derive inequalities for the modulus of derivative of f (z), |f'(0)| by assuming that the f(z) function is also holomorphic at the boundary point z = 0 on the real axis with f(0)=Rf(i).