On the multivalency of certain analytic functions

We prove several relations of the type | arg { z f ″ ( z ) / f ′ ( z ) } | ≤ | arg { f ′ ( z ) } | for functions satisfying some geometric conditions. MSC: 30C45, 30C80.

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2014; no. 1; pp. 1 - 9
Main Authors: Nunokawa, Mamoru, Sokół, Janusz
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 24.09.2014
Springer Nature B.V
Subjects:
Analysis
Analytic functions
Applications of Mathematics
Inequalities
Mathematics
Mathematics and Statistics
Recent Advances in Inequalities and Applications from Real and Complex Analysis
starlike
univalent
differential subordination
strongly starlike
multivalent
convex
analytic
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Description
Summary:We prove several relations of the type | arg { z f ″ ( z ) / f ′ ( z ) } | ≤ | arg { f ′ ( z ) } | for functions satisfying some geometric conditions. MSC: 30C45, 30C80.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2014-357