Starlikeness and convexity of a class of analytic functions

Nikola Tuneski and Hüseyin Irmak

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-8

Abstract:

Let be the class of analytic functions in the unit disk that are normalized with f ( 0 ) = f′ ( 0 ) − 1 = 0 and let − 1 ≤ B < A ≤ 1 . In this paper we study the class G λ , α = { f ∈ : | (1 − α + α z f ″ ( z ) / f′ ( z )) / z f′ ( z ) / f ( z ) − ( 1 − α ) | < λ , z ∈ } , 0 ≤ α ≤ 1 , and give sharp sufficient conditions that embed it into the classes S ∗ [ A , B ] = { f ∈ : z f′ ( z ) / f ( z ) ≺ (1 + A z) / (1 + B z) } and K ( δ ) = { f ∈ : 1 + z f ″ ( z ) / f′ ( z ) ≺ ( 1 − δ ) ( 1 + z ) / ( 1 − z ) + δ } , where “ ≺ †denotes the usual subordination. Also, sharp upper bound of | a 2 | and of the Fekete-Szegö functional | a 3 − μ a 2 2 | is given for the class G λ , α .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:038089

DOI: 10.1155/IJMMS/2006/38089

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