### Abstract

We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ^{∞}
_{n=2} a _{n}z^{n} in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: D^{k} _{α,β,λ},f(z) = z + Σ^{∞} _{n=2}[β(n-1)(λ-α) + 1]^{k}a_{n}z ^{n}, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

Original language | English |
---|---|

Pages (from-to) | 299-308 |

Number of pages | 10 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 33 |

Issue number | 3 |

Publication status | Published - Jun 2009 |

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### Keywords

- Al-Oboudi operator
- Differential operator
- Hadamard product
- Integral operator
- Salagean operator

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Far East Journal of Mathematical Sciences*,

*33*(3), 299-308.

**On subclasses for generalized operators of complex order.** / Darus, Maslina; Ibrahim, Rabha W.

Research output: Contribution to journal › Article

*Far East Journal of Mathematical Sciences*, vol. 33, no. 3, pp. 299-308.

}

TY - JOUR

T1 - On subclasses for generalized operators of complex order

AU - Darus, Maslina

AU - Ibrahim, Rabha W.

PY - 2009/6

Y1 - 2009/6

N2 - We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ∞ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ∞ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

AB - We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ∞ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ∞ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

KW - Al-Oboudi operator

KW - Differential operator

KW - Hadamard product

KW - Integral operator

KW - Salagean operator

UR - http://www.scopus.com/inward/record.url?scp=67650889312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650889312&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67650889312

VL - 33

SP - 299

EP - 308

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 3

ER -