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

@inproceedings{AlShaqsi2009OnCS,
title={On Certain Subclasses of Analytic Functions Defined by a Multiplier Transformation with Two Parameters},
author={K. Al-Shaqsi and Maslina Darus},
year={2009}
}

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… CONTINUE READING