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Subordination and superordination of certain linear operator on meromorphic functions

M. K. AoufT. M. Seoudy — 2010

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained.

Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

R. M. El-AshwahM. K. AoufS. M. El-Deeb — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In this paper we introduce and investigate three new subclasses of p -valent analytic functions by using the linear operator D λ , p m ( f * g ) ( z ) . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for ( n , θ ) -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

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

M. K. AoufA. ShamandyA. O. MostafaS. 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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