Fekete–Szegö problem for starlike and convex functions of complex order

For nonzero complex b let F n ( b ) denote the class of normalized univalent functions f satisfying Re  [ 1 + ( z ( D n f ) ′ ( z ) / D n f ( z ) − 1 ) / b ] > 0 in the unit disk U , where D n f denotes the Ruscheweyh derivative of f . Sharp bounds for the Fekete–Szegö functional | a 3 − μ a 2 2...

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Bibliographic Details
Published in:Applied mathematics letters 2010-07, Vol.23 (7), p.777-782
Main Authors: Kanas, S., Darwish, H.E.
Format: Article
Language:English
Subjects:
Coefficient estimates
Convex and starlike functions of complex order
Exact sciences and technology
Fekete–Szegö problem
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ruscheweyh derivative
Sciences and techniques of general use
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Summary:For nonzero complex b let F n ( b ) denote the class of normalized univalent functions f satisfying Re  [ 1 + ( z ( D n f ) ′ ( z ) / D n f ( z ) − 1 ) / b ] > 0 in the unit disk U , where D n f denotes the Ruscheweyh derivative of f . Sharp bounds for the Fekete–Szegö functional | a 3 − μ a 2 2 | are obtained.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2010.03.008