The Combined Coefficient Inequalities for Subordinate Functions

Let f ( z ) = ∑ n = 1 ∞ a n z n be a conformal mapping of the unit disk D onto a domain starlike with respect to the origin. In this note, we prove that if g ( z ) = ∑ n = 1 ∞ b n z n is analytic in D and is subordinate to f ( z );  then, some coefficient inequalities involving a n and b n hold for...

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Bibliographic Details
Published in:Computational methods and function theory 2018-09, Vol.18 (3), p.455-461
Main Author: Li, Jian-Lin
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Conformal mapping
Functions of a Complex Variable
Inequalities
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:Let f ( z ) = ∑ n = 1 ∞ a n z n be a conformal mapping of the unit disk D onto a domain starlike with respect to the origin. In this note, we prove that if g ( z ) = ∑ n = 1 ∞ b n z n is analytic in D and is subordinate to f ( z );  then, some coefficient inequalities involving a n and b n hold for all n . The results here extend the known results in a reasonable manner.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-018-0232-8