The Fekete-Szegö inequality for close-to-convex functions with respect to a certain starlike function dependent on a real parameter

Given α ∈ [ 0 , 1 ] , let g α ( z ) : = z / ( 1 − α z ) 2 , z ∈ D : = { z ∈ C : | z | < 1 } . An analytic standardly normalized function f in D is called close-to-convex with respect to g α if there exists δ ∈ ( − π / 2 , π / 2 ) such that Re { e i δ z f ′ ( z ) g α ( z ) } > 0 , z ∈ D . For t...

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Bibliographic Details
Published in:Journal of inequalities and applications 2014-02, Vol.2014 (1), p.1-16, Article 65
Main Authors: Kowalczyk, Bogumiła, Lecko, Adam
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Inequalities
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:Given α ∈ [ 0 , 1 ] , let g α ( z ) : = z / ( 1 − α z ) 2 , z ∈ D : = { z ∈ C : | z | < 1 } . An analytic standardly normalized function f in D is called close-to-convex with respect to g α if there exists δ ∈ ( − π / 2 , π / 2 ) such that Re { e i δ z f ′ ( z ) g α ( z ) } > 0 , z ∈ D . For the class C ( g α ) of all close-to-convex functions with respect to g α , the Fekete-Szegö problem is studied. MSC: 30C45.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2014-65