Wyniki wyszukiwania

1

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Properties of functions concerned with Caratheodory functions

100%

Nunokawa M., Duman E. Y., Owa S.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

|

2013

|

tom 67

|

nr 2

EN

Let \(\mathcal{P}_n\) denote the class of analytic functions \(p(z)\) of the form \(p(z)=1+c_nz^n+c_{n+1}z^{n+1}+\dots\) in the open unit disc \(\mathbb{U}\). Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for \(p(z)\) concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

2

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

EN

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.

3

Hardy class of functions defined by the Salagean operator

100%

Niwa N., Jimbo T., Owa S.

Annales Polonici Mathematici

|

1998

|

tom 69

|

nr 1

25-30

EN

We derive some properties of the Hardy class of analytic functions defined by the Salagean operator.

4

Convex meromorphic mappings

100%

Livingston A.

Annales Polonici Mathematici

|

1994

|

tom 59

|

nr 3

275-291

EN

We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.

5

Starlikeness of functions satisfying a differential inequality

88%

Ali R., Ponnusamy S., Singh V.

Annales Polonici Mathematici

|

1995

|

tom 61

|

nr 2

135-140

EN

In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.

Ograniczanie wyników

3 Annales Polonici Mathematici

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

2 Owa S.

1 Ali R.

1 Aouf M. K.

1 Duman E. Y.

1 Jimbo T.

1 Livingston A.

1 Madian S. M.

1 Mostafa A. O.

1 Niwa N.

1 Nunokawa M.

1 Ponnusamy S.

1 Shamandy A.

1 Singh V.

1 2013

1 2010

1 1998

1 1995

1 1994

Properties of functions concerned with Caratheodory functions

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

Hardy class of functions defined by the Salagean operator

Convex meromorphic mappings

Starlikeness of functions satisfying a differential inequality