### 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 letσ_{p,k} denote the class of Meromorphic functions in {double strock}* = {double strock}\{0}· In this paper, we introduce and study the classes of functions z^{p+1}f(z) ∈ A, such that f(z) ∈ {double strock}_{p,k} We also introduce and study the class V^{α,β}
_{λ,κ} (n, μ, δ, ξ, ∈) of functions f(z) ∈ (_{p,} satisfying where δ ≥ 0, λ ≥ 0, ξ ∈ (0, 1], ∈ ∈ [0,1) and D^{n}
_{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 language | English |
---|---|

Pages (from-to) | 112-121 |

Number of pages | 10 |

Journal | International Journal of Applied Mathematics and Statistics |

Volume | 23 |

Issue number | D11 |

Publication status | Published - 2011 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**A different approach to normalized analytic functions through meromorphic functions defined by extended multiplier transformations operator.** / Darus, Maslina; Faisal, Imran.

Research output: Contribution to journal › Article

*International Journal of Applied Mathematics and Statistics*, vol. 23, no. D11, pp. 112-121.

}

TY - JOUR

T1 - A different approach to normalized analytic functions through meromorphic functions defined by extended multiplier transformations operator

AU - Darus, Maslina

AU - Faisal, Imran

PY - 2011

Y1 - 2011

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

UR - http://www.scopus.com/inward/record.url?scp=79957918209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957918209&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 112

EP - 121

JO - International Journal of Applied Mathematics and Statistics

JF - International Journal of Applied Mathematics and Statistics

SN - 0973-1377

IS - D11

ER -