Geodesic
Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 54 (2010) no. 1.

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Let A denote the class of analytic functions with the normalization f(0)=f^'(0)-1=0 in the open unit disc U={z:| z| lt;1}.  Set f_λ^n(z)=z+∑_k=2^∞[1+λ (k-1)]^nz^k (n∈ N_0; λ≥ 0; z∈ U), and define f_λ ,μ^n in terms of the Hadamard product f_λ^n(z)∗ f_λ ,μ^n=z/(1-z)^μ (μ gt;0; z∈ U). In this paper, we introduce several subclasses of analytic functions defined by means of the operator I_λ ,μ^n:A⟶ A, given by I_λ ,μ^nf(z)=f_λ ,μ^n(z)∗ f(z) (f∈ A; n∈ N_0; λ≥ 0; μ gt;0). Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
Keywords: Analytic, Hadamard product, starlike, convex 
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Aouf, M. K.; Shamandy, A.; Mostafa, A. O.; Madian, S. M. Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 54 (2010) no. 1. http://geodesic.mathdoc.fr/item/AUM_2010_54_1_a3/

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