scholarly journals Applications of a Multiplier Transformation and Ruscheweyh Derivative for Obtaining New Strong Differential Subordinations

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1312
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Ruscheweyh Derivative ◽  
Differential Subordinations ◽  
Multiplier Transformation

Here, we study strong differential subordinations for the extended new operator IRλ,lm defined by the Hadamard product of the extended multiplier transformation Im,λ,l and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions Anζ∗={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}, by IRλ,lm:Anζ∗→Anζ∗, IRλ,lmfz,ζ=Im,λ,l∗Rmfz,ζ.

scholarly journals On Certain Class of Analytic Functions Related to Cho-Kwon-Srivastava Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
F. Ghanim ◽  
M. Darus
Keyword(s):  
Analytic Functions ◽  
Meromorphic Functions ◽  
Hadamard Product ◽  
Similar Transformation ◽  
Multiplier Transformation

Motivated by a multiplier transformation and some subclasses of meromorphic functions which were defined by means of the Hadamard product of the Cho-Kwon-Srivastava operator, we define here a similar transformation by means of the Ghanim and Darus operator. A class related to this transformation will be introduced and the properties will be discussed.

scholarly journals Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2487
Author(s):  
Alina Alb Lupaş ◽  
Georgia Oros
Keyword(s):  
Analytic Functions ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
New Approach ◽  
Ruscheweyh Derivative ◽  
Differential Superordination ◽  
Strong Differential Subordination ◽  
Extended Operator ◽  
Dual Notion ◽  
Differential Subordinations

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

scholarly journals On a certain subclass of analytic functions defined by a generalized S˘al˘agean operator and Ruscheweyh derivative

2012 ◽  
Vol 28 (2) ◽  
pp. 183-190
Author(s):  
ALINA ALB LUPAS ◽  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Ruscheweyh Derivative ◽  
Differential Subordinations

In the present paper we define a new operator using the generalized Sal˘ agean and Ruscheweyh operators. Denote by ˘ RDm λ,α the operator given by RDm λ,α : An → An, RDm λ,αf(z) = (1 − α)Rmf(z) + αDm λ f(z), z ∈ U, where Rmf(z) denote the Ruscheweyh derivative, Dm λ f(z) is the generalized Sal˘ agean operator and ˘ An = {f ∈ H(U) : f(z) = z +an+1z n+1 +. . . , z ∈ U} is the class of normalized analytic functions. A certain subclass, denoted by RDm (δ, λ, α) , of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class RDm (δ, λ, α) . Also, several differential subordinations are established regarding the operator RDm λ,α.

scholarly journals Some Properties for Strong Differential Subordination of Analytic Functions Involving Ruscheweyh Derivative Operator

2020 ◽  
pp. 63-70
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Derivative Operator ◽  
Closed Unit Disk ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Strong Differential Subordination ◽  
Differential Subordinations

In this paper, we introduce and study some properties for strong differential subordinations of analytic functions associated with Ruscheweyh derivative operator defined in the open unit disk and closed unit disk of the complex plane.

scholarly journals On new classes of analytic functions with negative coefficients

1984 ◽  
Vol 7 (4) ◽  
pp. 719-730 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Ruscheweyh Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities

We introduce the classesKn*of analytic functions with negative coefficients by using thenth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functionsf(z)inKn*. Further we consider the modified Hadamard product of functionsfi(z)inKni*(n=1,2,…,m).

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