A different approach to normalized analytic functions through meromorphic functions defined by extended multiplier transformations operator

Maslina Darus, Imran Faisal

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1 Citation (Scopus)

Abstract

Let A(n) denote the class of analytic functions f, in the open unit disk U = {z : |z| < 1} normalized by f(0) = f'(0)-1 = 0, and letσp,k denote the class of Meromorphic functions in {double strock}* = {double strock}\{0}· In this paper, we introduce and study the classes of functions zp+1f(z) ∈ A, such that f(z) ∈ {double strock}p,k We also introduce and study the class Vα,β λ,κ (n, μ, δ, ξ, ∈) of functions f(z) ∈ (p, satisfying where δ ≥ 0, λ ≥ 0, ξ ∈ (0, 1], ∈ ∈ [0,1) and Dn λ(α, β, μ)f(z): A →A, is the Extended Multiplier Transformations Operator, newly defined as follows Several inclusion, subordination, and superordination properties have been discussed for the above said classes of normalized analytic and meromorphic functions.

Original languageEnglish
Pages (from-to)112-121
Number of pages10
JournalInternational Journal of Applied Mathematics and Statistics
Volume23
Issue numberD11
Publication statusPublished - 2011

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Multiplier Transformation
Meromorphic Function
Mathematical operators
Analytic function
Operator
Denote
Subordination
Unit Disk
Inclusion
Class

Keywords

  • Analytic functions
  • Differential subordination
  • Differential Superordination
  • Meromorphic functions
  • Normalize analytic functions

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "Let A(n) denote the class of analytic functions f, in the open unit disk U = {z : |z| < 1} normalized by f(0) = f'(0)-1 = 0, and letσp,k denote the class of Meromorphic functions in {double strock}* = {double strock}\{0}· In this paper, we introduce and study the classes of functions zp+1f(z) ∈ A, such that f(z) ∈ {double strock}p,k We also introduce and study the class Vα,β λ,κ (n, μ, δ, ξ, ∈) of functions f(z) ∈ (p, satisfying where δ ≥ 0, λ ≥ 0, ξ ∈ (0, 1], ∈ ∈ [0,1) and Dn λ(α, β, μ)f(z): A →A, is the Extended Multiplier Transformations Operator, newly defined as follows Several inclusion, subordination, and superordination properties have been discussed for the above said classes of normalized analytic and meromorphic functions.",
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AU - Darus, Maslina

AU - Faisal, Imran

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N2 - Let A(n) denote the class of analytic functions f, in the open unit disk U = {z : |z| < 1} normalized by f(0) = f'(0)-1 = 0, and letσp,k denote the class of Meromorphic functions in {double strock}* = {double strock}\{0}· In this paper, we introduce and study the classes of functions zp+1f(z) ∈ A, such that f(z) ∈ {double strock}p,k We also introduce and study the class Vα,β λ,κ (n, μ, δ, ξ, ∈) of functions f(z) ∈ (p, satisfying where δ ≥ 0, λ ≥ 0, ξ ∈ (0, 1], ∈ ∈ [0,1) and Dn λ(α, β, μ)f(z): A →A, is the Extended Multiplier Transformations Operator, newly defined as follows Several inclusion, subordination, and superordination properties have been discussed for the above said classes of normalized analytic and meromorphic functions.

AB - Let A(n) denote the class of analytic functions f, in the open unit disk U = {z : |z| < 1} normalized by f(0) = f'(0)-1 = 0, and letσp,k denote the class of Meromorphic functions in {double strock}* = {double strock}\{0}· In this paper, we introduce and study the classes of functions zp+1f(z) ∈ A, such that f(z) ∈ {double strock}p,k We also introduce and study the class Vα,β λ,κ (n, μ, δ, ξ, ∈) of functions f(z) ∈ (p, satisfying where δ ≥ 0, λ ≥ 0, ξ ∈ (0, 1], ∈ ∈ [0,1) and Dn λ(α, β, μ)f(z): A →A, is the Extended Multiplier Transformations Operator, newly defined as follows Several inclusion, subordination, and superordination properties have been discussed for the above said classes of normalized analytic and meromorphic functions.

KW - Analytic functions

KW - Differential subordination

KW - Differential Superordination

KW - Meromorphic functions

KW - Normalize analytic functions

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