On Univalence Criteria for Analytic Functions Defined by Multiplier Transformation and Ruscheweyh Derivative

2014 ◽  
Vol 7 (1) ◽  
pp. 14-21
Author(s):  
Alina Alb Lupas
Keyword(s):  
Analytic Functions ◽  
Ruscheweyh Derivative ◽  
Univalence Criteria ◽  
Multiplier Transformation

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 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 Kudriasov Type Univalence Criteria for Some Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Virgil Pescar ◽  
Nicoleta Breaz
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Univalence Criteria

We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
M. P. Jeyaraman ◽  
T. K. Suresh
Keyword(s):  
Analytic Functions ◽  
Multiplier Transformation

The main object of the present paper is to investigate several interesting subordination properties and a sharp inclusion relationship for certain subclass of multivalent analytic functions, which are defined here by the generalized multiplier transformation. Relevant connections of the results which are presented in this paper with various known results are also considered.

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