scholarly journals ON CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS IN THE UNIT DISC I

1995 ◽  
Vol 26 (4) ◽  
pp. 299-312
Author(s):  
M. K. AOUF ◽  
A. SHAMANDY ◽  
M. F. YASSEN
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Closure Theorems ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

The object of the present paper is to derive several interesting proper- ties of the class $P_n(\alpha, \beta, \gamma)$ consisting of analytic and univalent functions with neg- ative coefficients. Coefficient estimates, distortion theorems and closure theorems of functions in the class $P_n(\alpha, \beta, \gamma)$ are determined. Also radii of close-to-convexity, starlikeness and convexity and integral operators are determined.

scholarly journals Some properties of a class of analytic functions involving a new generalized differential operator

2019 ◽  
Vol 38 (6) ◽  
pp. 33-42 ◽  
Author(s):  
A. A. Amourah ◽  
Feras Yousef
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

scholarly journals A GENERALIZATION OF CERTAIN CLASSES OF ANALYTIC FUNCTIONS

1994 ◽  
Vol 25 (1) ◽  
pp. 41-51
Author(s):  
M. K. AOUF
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Special Classes

There are many classes of analytic functions in the unit disc $U$. We consider about the special classes $S^*_\lambda(A,B,\alpha,\beta)$ and $C^*_\lambda(A,B,\alpha,\beta)$( $-1\le A < B \le 1$, $0 < B \le 1$, $0 \le \alpha < 1$ and $0 < \beta \le 1$) of analytic functions in the unit disc $U$. And the purpose of this paper is to study the classes $S^*_\lambda(A,B,\alpha,\beta)$ and $C^*_\lambda(A,B,\alpha,\beta)$. We prove some distortion theorems and some coefficient estimates for these classes $S^*_\lambda(A,B,\alpha,\beta)$ and $C^*_\lambda(A,B,\alpha,\beta)$.

scholarly journals Meromorphic univalent functions with positive coefficients

1985 ◽  
Vol 32 (2) ◽  
pp. 161-176 ◽  
Author(s):  
M.L. Mogra ◽  
T.R. Reddy ◽  
O.P. Juneja
Keyword(s):  
Univalent Functions ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Positive Coefficients ◽  
Meromorphic Univalent Functions

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

scholarly journals A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2837-2849
Author(s):  
Zainab Esa ◽  
H.M. Srivastava ◽  
Adem Kılıçman ◽  
Rabha Ibrahim
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Univalent Functions ◽  
Complex Domain ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Fractional Derivative Operators ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass P?,?(k,?,?) of analytic and univalent functions in the open unit disk U. In particular, for functions in the class P?,?(k,?,?), we derive sufficient coefficient inequalities and coefficient estimates, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class P?,?(k,?,?) are also pointed out.

scholarly journals Properties on a subclass of univalent functions defined by using a multiplier transformation and Ruscheweyh derivative

2015 ◽  
Vol 23 (1) ◽  
pp. 9-24
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Ruscheweyh Derivative ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Multiplier Transformation

AbstractIn this paper we have introduced and studied the subclass ℛ𝒥 (d, α, β) of univalent functions defined by the linear operator $RI_{n,\lambda ,l}^\gamma f(z)$ defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n, λ, l) f(z), as $RI_{n,\lambda ,l}^\gamma :{\cal A} \to {\cal A}$, $RI_{n,\lambda ,l}^\gamma f(z) = (1 - \gamma )R^n f(z) + \gamma I(n,\lambda ,l)f(z)$, z ∈ U, where 𝒜n ={f ∈ ℋ(U) : f(z) = z + an+1zn+1 + . . . , z ∈ U}is the class of normalized analytic functions with 𝒜1 = 𝒜. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class ℛ𝒥(d, α, β).

scholarly journals Comprehensive family of uniformly analytic functions

2005 ◽  
Vol 36 (3) ◽  
pp. 243-254 ◽  
Author(s):  
B. A. Frasin
Keyword(s):  
Analytic Functions ◽  
Integral Operators ◽  
Hadamard Products ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Alpha Beta ◽  
Distortion Theorems

We introduce the subclass $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ of analytic functions with negative coefficients. Coefficient inequalities, distortion theorems, closure theorems, radii of close-to-convexity, starlikeness, and convexity for functions belonging to the class $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ are obtained. We also determine integral operators for functions in this class and some properties involving modified Hadamard products of several functions belonging to the class $ \mathcal{U}_{\mathcal{T}}^*(\Phi ,\Psi ;\alpha ,\beta ) $.

Some Properties of the Class of Univalent Functions Involving a New Generalized Differential Operator

2016 ◽  
Vol 13 (10) ◽  
pp. 6797-6799
Author(s):  
A. A Amourah ◽  
T Al-Hawary ◽  
M Darus
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Univalent Functions ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

The main purpose of this paper is to introduce new generalized differential operator Aμm, λ(α,β)f(z) defined in the open unit disc U = {z ∈ : |z| < 1}. We then, using this operator to introduce novel subclass Ωm*(δ,λ,α,β,b) by using the operator Aμm, λ(α,β)f(z). Then, we discuss coefficient estimates growth and distortion theorems, closure theorems and integral operator.

scholarly journals A Certain Subclass of Analytic and Univalent Functions Defined by Hadamard Product

2019 ◽  
pp. 87-99
Author(s):  
Dhirgam Allawy Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Hadamard Product ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Analytic And Univalent Functions

In this paper, we present a new subclass AD(l, g, a, b) of analytic univalent functions in the open unit disk U. We establish some interesting properties like, coefficient estimates, closure theorems, extreme points, growth and distortion theorem and radius of starlikeness and convexity.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals A Class of p-valent Functions in the Punctured Disc

2019 ◽  
pp. 473-481
Author(s):  
Olubunmi A. Fadipe-Joseph ◽  
K. O. Dada
Keyword(s):  
Differential Operator ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

Motivated by Aouf differential operator, a class $F_{\lambda, p}^{n}\left ( \alpha , \beta , \gamma \right )$ of p-valent functions in the punctured disc $U^{*}=\left \{ z:0<\left | z \right |<1 \right \}=U\setminus \left \{ 0 \right \} $ is defined. The coefficient estimates, growth and distortion theorems for the class are obtained.

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