### Abstract

The authors have recently introduced a new generalised derivatives operator μ_{λ1,λ2}
^{n,m}, which generalised many well-known operators studied earlier by many different authors. The trend of finding new operators such as the differential or the integral operators has attracted many researchers and in fact, has become necessary to some of the researchers. The aim of this paper is to use the equality relation (1+n)μ_{λ1,λ2}
^{n+1,m}f(z) = z(μμ_{λ1,λ2}
^{n,m}f(z)))′ + n(μμ_{λ1,λ2}
^{n,m} f(z)), to discuss some interesting results using the technique of differential subordination. The results include the subordination and the inclusion. Whenever n = 0, λ_{2} = 0 we have results given by Oros [10].

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

Title of host publication | 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Proceedings |

Pages | 580-592 |

Number of pages | 13 |

DOIs | |

Publication status | Published - 2009 |

Event | 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Coimbatore Duration: 9 Dec 2009 → 11 Dec 2009 |

### Other

Other | 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 |
---|---|

City | Coimbatore |

Period | 9/12/09 → 11/12/09 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Software

### Cite this

*2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Proceedings*(pp. 580-592). [5393410] https://doi.org/10.1109/NABIC.2009.5393410

**Differential subordination associated with generalised derivative operator.** / Al-Abbadi, Mamoun Harayzeh; Darus, Maslina.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Proceedings.*, 5393410, pp. 580-592, 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009, Coimbatore, 9/12/09. https://doi.org/10.1109/NABIC.2009.5393410

}

TY - GEN

T1 - Differential subordination associated with generalised derivative operator

AU - Al-Abbadi, Mamoun Harayzeh

AU - Darus, Maslina

PY - 2009

Y1 - 2009

N2 - The authors have recently introduced a new generalised derivatives operator μλ1,λ2 n,m, which generalised many well-known operators studied earlier by many different authors. The trend of finding new operators such as the differential or the integral operators has attracted many researchers and in fact, has become necessary to some of the researchers. The aim of this paper is to use the equality relation (1+n)μλ1,λ2 n+1,mf(z) = z(μμλ1,λ2 n,mf(z)))′ + n(μμλ1,λ2 n,m f(z)), to discuss some interesting results using the technique of differential subordination. The results include the subordination and the inclusion. Whenever n = 0, λ2 = 0 we have results given by Oros [10].

AB - The authors have recently introduced a new generalised derivatives operator μλ1,λ2 n,m, which generalised many well-known operators studied earlier by many different authors. The trend of finding new operators such as the differential or the integral operators has attracted many researchers and in fact, has become necessary to some of the researchers. The aim of this paper is to use the equality relation (1+n)μλ1,λ2 n+1,mf(z) = z(μμλ1,λ2 n,mf(z)))′ + n(μμλ1,λ2 n,m f(z)), to discuss some interesting results using the technique of differential subordination. The results include the subordination and the inclusion. Whenever n = 0, λ2 = 0 we have results given by Oros [10].

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=77949650897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949650897&partnerID=8YFLogxK

U2 - 10.1109/NABIC.2009.5393410

DO - 10.1109/NABIC.2009.5393410

M3 - Conference contribution

SN - 9781424456123

SP - 580

EP - 592

BT - 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Proceedings

ER -