Fekete–Szegö Problem for a Certain Subclass of Close-to-convex Functions

Given a starlike function g ∈ S ∗ , an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists δ ∈ ( - π / 2 , π / 2 ) such that Re e i δ z f ′ ( z ) g ( z ) > 0 , z ∈ D . For the class C ( h ) of all close-to-convex functions with...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2015-10, Vol.38 (4), p.1393-1410
Main Authors: Kowalczyk, Bogumiła, Lecko, Adam
Format: Article
Language:English
Subjects:
Applications of Mathematics
Convex analysis
Mathematics
Mathematics and Statistics
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Summary:Given a starlike function g ∈ S ∗ , an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists δ ∈ ( - π / 2 , π / 2 ) such that Re e i δ z f ′ ( z ) g ( z ) > 0 , z ∈ D . For the class C ( h ) of all close-to-convex functions with respect to h ( z ) : = z / ( 1 - z ) , z ∈ D , a Fekete–Szegö problem is examined.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-014-0091-z