On the Schwarz lemma at the upper half plane | Zendy

Bülent Nafi Örnek | Zendy

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On the Schwarz lemma at the upper half plane

Author(s) -

Bülent Nafi Örnek

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).

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