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

Rabha El-Ashwah, Mohamed Aouf, S. 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.

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

Mohamed Aouf, Rabha 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 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 relationships between classes of functions defined by subordination

Jacek Dziok (2011)

Annales Polonici Mathematici

The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. Dewan, Sunil Hans (2011)

Annales UMCS, Mathematica

In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.

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