Starlikeness and convexity of a class of analytic functions
2006 ◽
Vol 2006
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pp. 1-8
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Letbe the class of analytic functions in the unit disk that are normalized withf(0)=f′(0)−1=0and let−1≤B<A≤1. In this paper we study the classGλ,α={f∈:|(1−α+αzf″(z)/f′(z))/zf′(z)/f(z)−(1−α)|<λ,z∈},0≤α≤1,and give sharp sufficient conditions that embed it into the classesS∗[A,B]={f∈:zf′(z)/f(z)≺(1+Az)/(1+Bz)}andK(δ)={f∈:1+zf″(z)/f′(z)≺(1−δ)(1+z)/(1−z)+δ}, where “≺” denotes the usual subordination. Also, sharp upper bound of|a2|and of the Fekete-Szegö functional|a3−μa22|is given for the classGλ,α.
2006 ◽
Vol 4
(1)
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pp. 73-84
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2019 ◽
Vol 100
(3)
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pp. 458-469
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