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Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator

M. Aouf;  A. Shamandy;  A. Mostafa;  S. Madian — 2010

Annales UMCS, Mathematica

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| < 1}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

M. K. Aouf;  A. Shamandy;  A. O. Mostafa;  S. M. Madian — 2010

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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 < 1 } .  Set f λ n ( z ) = z + ∑ k = 2 ∞ [ 1 + λ ( k - 1 ) ] n z 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 > 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 n f ( z ) = f λ , μ n ( z ) * f ( z ) ( f ∈ A ; n ∈ N 0 ; λ ≥ 0 ; μ > 0 ) . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Subordination results for some subclasses of analytic functions

R. M. El-Ashwah;  M. K. Aouf;  A. Shamandy;  E. E. Ali — 2011

Mathematica Bohemica

We introduce two classes of analytic functions related to conic domains, using a new linear multiplier Dziok-Srivastava operator D λ , ℓ n . q , s ( n ∈ ℕ 0 = { 0 , 1 , ⋯ } , q ≤ s + 1 ; q , s ∈ ℕ 0 , 0 ≤ α < 1 , λ ≥ 0 , ℓ ≥ 0 ) . Basic properties of these classes are studied, such as coefficient bounds. Various known or new special cases of our results are also pointed out. For these new function classes, we establish subordination theorems and also deduce some corollaries of these results.

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