### Abstract

The authors have recently introduced a new generalized derivative operator μ^{n,m}
_{λ1},_{λ2} that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0, λ_{2} = 0, we obtain the results of Oros [11].

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

Pages (from-to) | 209-222 |

Number of pages | 14 |

Journal | Miskolc Mathematical Notes |

Volume | 13 |

Issue number | 2 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Analytic function
- Best dominant
- Convex function
- Derivative operator
- Differential subordination
- Dominant
- Hadamard product (or convolution)
- Univalent function

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Control and Optimization
- Discrete Mathematics and Combinatorics
- Numerical Analysis

### Cite this

*Miskolc Mathematical Notes*,

*13*(2), 209-222.

**Differential subordination for a certain generalized operator.** / Al-Abbadi, M. H.; Darus, Maslina.

Research output: Contribution to journal › Article

*Miskolc Mathematical Notes*, vol. 13, no. 2, pp. 209-222.

}

TY - JOUR

T1 - Differential subordination for a certain generalized operator

AU - Al-Abbadi, M. H.

AU - Darus, Maslina

PY - 2012

Y1 - 2012

N2 - The authors have recently introduced a new generalized derivative operator μn,m λ1,λ2 that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0, λ2 = 0, we obtain the results of Oros [11].

AB - The authors have recently introduced a new generalized derivative operator μn,m λ1,λ2 that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0, λ2 = 0, we obtain the results of Oros [11].

KW - Analytic function

KW - Best dominant

KW - Convex function

KW - Derivative operator

KW - Differential subordination

KW - Dominant

KW - Hadamard product (or convolution)

KW - Univalent function

UR - http://www.scopus.com/inward/record.url?scp=84877339467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877339467&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 209

EP - 222

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

SN - 1787-2405

IS - 2

ER -