On the quotient of the representations of convexity and starlikeness | Zendy

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On the quotient of the representations of convexity and starlikeness

Author(s) -

Tuneski Nikola

Publication year - 2003

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310015

Subject(s) - mathematics , unit disk , convexity , quotient , lemma (botany) , class (philosophy) , unit (ring theory) , combinatorics , function (biology) , analytic function , pure mathematics , mathematical analysis , ecology , mathematics education , poaceae , artificial intelligence , evolutionary biology , computer science , financial economics , economics , biology

Let f ( z ) = z + a 2 z 2 + … be an analytic function in the unit disk = { z : | z | < 1}. Such a function belongs to the class G b defined by Silverman if the quotient of the analytic representations of convexity and starlikeness of the function maps the unit disk into a disk with center 1 and radius b . By using the Jack lemma we analyze the relation between the class G b and the class S *[ A,B ] and its subclasses.

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