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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.

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