scholarly journals Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

2021 ◽  
pp. 2667-2675
Author(s):  
Mohammed Hadi Lafta
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Growth Theorem ◽  
Closure Theorem ◽  
Major Target ◽  
Meromorphic Univalent Functions

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

scholarly journals On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 312
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained.

scholarly journals A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

2020 ◽  
pp. 1440-1445
Author(s):  
Faten Fakher Aubdulnabi ◽  
Kassim A. Jassim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

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 On Certain Subclasses of Meromorphic Functions with Positive and Fixed Second Coefficients Involving the Liu-Srivastava Linear Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
N. Magesh ◽  
N. B. Gatti ◽  
S. Mayilvaganan
Keyword(s):  
Linear Operator ◽  
Linear Combination ◽  
Hypergeometric Function ◽  
Meromorphic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Generalized Hypergeometric Function ◽  
Coefficient Estimates ◽  
Convex Linear Combination ◽  
Meromorphic Univalent Functions

We introduce and study a subclass ΣP(γ,k,λ,c) of meromorphic univalent functions defined by certain linear operator involving the generalized hypergeometric function. We obtain coefficient estimates, extreme points, growth and distortion inequalities, radii of meromorphic starlikeness, and convexity for the class ΣP(γ,k,λ,c) by fixing the second coefficient. Further, it is shown that the class ΣP(γ,k,λ) is closed under convex linear combination.

scholarly journals Subclass of p-valent Function with Negative Coefficients Applying Generalized Al-Oboudi Differential Operator

2021 ◽  
pp. 87-103
Author(s):  
Timilehin G. Shaba ◽  
Abd'gafar T. Tiamiyu ◽  
Ismaila O. Ibrahim ◽  
Abdullahi A. Ibrahim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Distortion Theorem ◽  
Negative Coefficient ◽  
Growth Theorem ◽  
Coefficient Inequalities ◽  
Generalized Differential

In this paper we introduce a new subclass $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ of $p$-valent functions with negative coefficient defined by Hadamard product associated with a generalized differential operator. Radii of close-to-convexity, starlikeness and convexity of the class $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ are obtained. Also, distortion theorem, growth theorem and coefficient inequalities are established.

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1(Suppl.)) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

We introduce and investigate a new general subclass ℋΣλ,μ(φ;Θ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

Faber polynomial coefficient estimates for a class of analytic bi-univalent functions involving a certain differential operator

2017 ◽  
Vol 10 (01) ◽  
pp. 1750016 ◽  
Author(s):  
Poonam Sharma
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial

In this paper, we define a sub-class of analytic bi-univalent functions associated with a certain differential operator [Formula: see text]. Bounds for the general Taylor–Maclaurin coefficients [Formula: see text] for the functions in this class are obtained. Estimates for the coefficient [Formula: see text] and the estimate for the functional [Formula: see text] for any real [Formula: see text], are also found. Results for the specific values of the parameters [Formula: see text], are also given mentioning some of the results obtained earlier.

scholarly journals MEROMORPHIC UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 81-88
Author(s):  
S. M. SARANGI ◽  
SUGUNA B. URALEGADDI
Keyword(s):  
Univalent Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Coefficient Inequalities ◽  
Meromorphic Univalent Functions

Coefficient inequalities, distortion theorem, extreme points and prop­ erty preserving integral operators are obtained for certam subclasses of meromor­phic starlike functions with negative coefficints. Convolutions of functions in these classes are also obtained.

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