scholarly journals On classes of meromorphic functions with fixed point and fixed second and finitely many coeeficients defined by q -Derivative

2020 ◽  
Vol 8 (1) ◽  
pp. 121-129
Author(s):  
G. E. Abo Elyazyd ◽  
A. M. Shahin ◽  
H. E. Darwish
Keyword(s):  
Fixed Point ◽  
Meromorphic Functions ◽  
Coefficient Estimates ◽  
Closure Theorems

Abstract: In this paper we consider the class functions with a fixed point The aim of the present paper is to drive several interesting properties as coefficient estimates, distortion M S ( , , c).The q    theorems, radii of starlikeness and convexity and closure theorems of f (z) in the class results are generalized to families with finitely many fixed coefficients

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 Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa ◽  
H. M. Zayed
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Convolution Properties

Making use of the operatorLυfor functions of the formfz=1/z+∑k=1∞akzk-1, which are analytic in the punctured unit discU∗={z:z∈Cand0<|z|<1}=U∖{0}, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses.

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.

On a subclass of uniformly convex functions with fixed second coefficient

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
H. E. Darwish
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Distortion Bounds ◽  
Closure Theorems

AbstractUsing of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.

scholarly journals On Meromorphic Functions Defined by a New Operator Containing the Mittag–Leffler Function

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 210 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Meromorphic Function ◽  
Hypergeometric Function ◽  
Meromorphic Functions ◽  
Hadamard Product ◽  
Linear Differential Operator ◽  
Extreme Points ◽  
Growth Coefficient ◽  
Closure Theorems ◽  
Linear Differential

This study defines a new linear differential operator via the Hadamard product between a q-hypergeometric function and Mittag–Leffler function. The application of the linear differential operator generates a new subclass of meromorphic function. Additionally, the study explores various properties and features, such as convex properties, distortion, growth, coefficient inequality and radii of starlikeness. Finally, the work discusses closure theorems and extreme points.

Fixed points of composite meromorphic functions and normal families

2004 ◽  
Vol 134 (4) ◽  
pp. 653-660 ◽  
Author(s):  
Walter Bergweiler
Keyword(s):  
Fixed Point ◽  
Meromorphic Function ◽  
Fixed Points ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Holomorphic Functions ◽  
Normal Families ◽  
The Family

We show that there exists a function f, meromorphic in the plane C, such that the family of all functions g holomorphic in the unit disc D for which f ∘ g has no fixed point in D is not normal. This answers a question of Hinchliffe, who had shown that this family is normal if Ĉ\f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic functions g such that f(g(z)) ≠ h(z) for some non-constant meromorphic function h.

scholarly journals Weighted sharing and uniqueness of memorphic functions with regard to multiplicity

2014 ◽  
Vol 45 (2) ◽  
pp. 165-177
Author(s):  
Pulak Sahoo ◽  
Biswajit Saha
Keyword(s):  
Fixed Point ◽  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Weighted Sharing

In the paper we study the uniqueness problems of meromorphic functions whose certain nonlinear differential polynomials share certain value or fixed point with finite weight and obtain two theorems which improve two recent results due to S.S. Bhoosnurmath and S.R. Kabbur [Tamkang J. Math., 44, 11-22, Spring 2013].

scholarly journals NEW SUBCLASS OF MEROMORPHIC FUNCTIONS BY THE GENERALIZATION OF THE q-DERIVATIVE OPERATOR

2021 ◽  
pp. 1461
Author(s):  
Mohammad Hassn Golmohammadi ◽  
Shahram Najafzadeh ◽  
Mohammad Reza Forutan
Keyword(s):  
Linear Combination ◽  
Meromorphic Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Partial Sum ◽  
New Class ◽  
Convex Linear Combination

In this paper, we introduce a new  class of meromorphic functions, using the exponent $ q $-derivative operator, and then look at it coefficient estimates, extreme points, convex linear combination, Radii of starlikeness, convexity and finally partial sum property are investigated.

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

2019 ◽  
Vol 69 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad A. Zaighum ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Extreme Point ◽  
Convex Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Closure Theorems

Abstract Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

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).

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