Radius Problems for Some Subclasses of Analytic Functions

In this work, we define the class M ( α ) of normalized analytic functions which satisfy the following two-sided inequality: 1 + α - π 2 sin α < R e z f ′ ( z ) f ( z ) < 1 + α 2 sin α | z | < 1 , where π / 2 ≤ α < π . We obtain a sufficient condition for functions to be in the class M (...

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Bibliographic Details
Published in:Complex analysis and operator theory 2017-10, Vol.11 (7), p.1639-1649
Main Authors: Kargar, R., Ebadian, A., Sokół, J.
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Mathematics
Mathematics and Statistics
Operator Theory
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Summary:In this work, we define the class M ( α ) of normalized analytic functions which satisfy the following two-sided inequality: 1 + α - π 2 sin α < R e z f ′ ( z ) f ( z ) < 1 + α 2 sin α | z | < 1 , where π / 2 ≤ α < π . We obtain a sufficient condition for functions to be in the class M ( α ) and solve several radius problems related to other well-known function classes.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-016-0584-x