Open AccessNote on some classes of holomorphic functions related to Jack’s and Schwarz’s lemma
Author(s) -
Miodrag Mateljević,
Nikola Mutavdžić,
Bülent Nafi Örnek
Publication year - 2022
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm200319006m
Subject(s) - holomorphic function , mathematics , lemma (botany) , connection (principal bundle) , unit (ring theory) , pure mathematics , combinatorics , algebra over a field , geometry , mathematics education , ecology , poaceae , biology
In this paper we discuss holomorphic mappings f of the unit disc U and corresponding index defined as If (z) = zf?(z) f(z). We are interested in finding bounds on the growth of functions f and related issues, if there are known some properties of If on U. Our main tool in accomplishing this connection is Jack?s lemma. As a special case, we got estimates on the growth of some classes of ?-starlike functions as well as some interesting generalisations.