On Certain Subclasses of Analytic Functions Defined by a Multiplier Transformation with Two Parameters

نویسندگان

  • K. Al-Shaqsi
  • M. Darus
چکیده

Let A denote the class of analytic functions with the normalization f(0) = f ′(0) − 1 = 0 in the open unit disk U = {z : |z| < 1}, set f b,λ(z) = z + ∞ ∑ k=2 (k + b 1 + b )n (k + λ− 1)! λ!(k − 1)! z k (n ∈ C, b ∈ C \ Z−, λ > −1; z ∈ U). and define (fn b,λ) (−1) in terms of the Hadamard product f b,λ(z) ∗ (f b,λ)(z) = z (1 − z)μ (μ > 0; z ∈ U). In this paper, the authors introduce several new subclasses of analytic functions defined by means of the operator In b,λ,μ : A → A, given by I b,λ,μf(z) = (f n b,λ) (−1) ∗ f(z) (f ∈ A;n ∈ C, b ∈ C \ Z−, λ > −1;μ > 0). Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered Mathematics Subject Classification: 30C45

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تاریخ انتشار 2009