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Inclusion properties of certain subclass of analytic functions defined by multiplier transformations

Mohamed AoufRabha El-Ashwah — 2009

Annales UMCS, Mathematica

Let A denote the class of analytic functions with normalization [...] in the open unit disk [...] Set [...] and define [...] in terms of the Hadamard product [...] In this paper, we introduce several new subclasses of analytic functions defined by means of the operator [...] [...] .Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

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

Rabha El-AshwahMohamed AoufS. El-Deeb — 2011

Annales UMCS, Mathematica

In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator Dmλ,p(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.

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