scholarly journals On a new subclass of harmonic univalent functions defined by multiplier transformation

2015 ◽  
Vol 19 (2) ◽  
pp. 75-87
Author(s):  
Saurabh Porwal
Keyword(s):  
Univalent Functions ◽  
Multiplier Transformation

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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 On Subclass of Meromorphic Univalent Functions Defined by Multiplier Transformation

2021 ◽  
Vol 32 (3) ◽  
pp. 15
Author(s):  
Mustafa Fawzy Kazem ◽  
Ahmed Khalaf Radhi
Keyword(s):  
Linear Combination ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
New Class ◽  
Convex Linear Combination ◽  
Multiplier Transformation ◽  
Meromorphic Univalent Functions

In this paper, we will investigate and discuss a new class of meromorphic univalent functions defined by multiplier transformation which is R(c, , y, ), as well as study the coefficient estimates and growth theorems, and then another line in this work, upon to get the close under the convex linear combination 

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta
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