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

100%

El-Ashwah R. M., Aouf M. K., El-Deeb S. M.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 1

In this paper we introduce and investigate three new subclasses of \(p\)-valent analytic functions by using the linear operator \(D_{\lambda,p}^m(f*g)(z)\). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for \((n,\theta)\)-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

100%

Aouf M. K., Shamandy A., Mostafa A. O., Madian S. M.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2010

tom 64

nr 1

Let \(A\) denote the class of analytic functions with the normalization \(f(0)=f^{\prime }(0)-1=0\) in the open unit disc \(U=\{z:\left\vert z\right\vert <1\}\). Set \[f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),\] and define \(f_{\lambda ,\mu }^{n}\) in terms of the Hadamard product \[f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). \] In this paper, we introduce several subclasses of analytic functions defined by means of the operator \(I_{\lambda ,\mu }^{n}:A\longrightarrow A\), given by \[ I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). \]Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Ograniczanie wyników

2 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2 Aouf M. K.

1 El-Ashwah R. M.

1 El-Deeb S. M.

1 Madian S. M.

1 Mostafa A. O.

1 Shamandy A.

1 2011

1 2010

Wyniki wyszukiwania

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

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