### Abstract

We define new classes of the family ε(Φ, ψ), in a unit disk U :={z ∈ ℂ, \z\ < 1}, as follows: for analytic functions F(z),Φ(z) and ψ(z) so that ∩{F(z)*Φ(z)/F(z)*Φ(z) } > 0, z ∈ U, F(z) *ψ(z) ≠ 0 where the operator * denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

Original language | English |
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Article number | 8 |

Journal | Journal of Inequalities in Pure and Applied Mathematics |

Volume | 10 |

Issue number | 1 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Fractional calculus
- Hadamard product
- Subordination

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Journal of Inequalities in Pure and Applied Mathematics*,

*10*(1), [8].

**Differential subordination results for new classes of the family ε(Φ, ψ).** / Ibrahim, Rabha W.; Darus, Maslina.

Research output: Contribution to journal › Article

*Journal of Inequalities in Pure and Applied Mathematics*, vol. 10, no. 1, 8.

}

TY - JOUR

T1 - Differential subordination results for new classes of the family ε(Φ, ψ)

AU - Ibrahim, Rabha W.

AU - Darus, Maslina

PY - 2009

Y1 - 2009

N2 - We define new classes of the family ε(Φ, ψ), in a unit disk U :={z ∈ ℂ, \z\ < 1}, as follows: for analytic functions F(z),Φ(z) and ψ(z) so that ∩{F(z)*Φ(z)/F(z)*Φ(z) } > 0, z ∈ U, F(z) *ψ(z) ≠ 0 where the operator * denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

AB - We define new classes of the family ε(Φ, ψ), in a unit disk U :={z ∈ ℂ, \z\ < 1}, as follows: for analytic functions F(z),Φ(z) and ψ(z) so that ∩{F(z)*Φ(z)/F(z)*Φ(z) } > 0, z ∈ U, F(z) *ψ(z) ≠ 0 where the operator * denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

KW - Fractional calculus

KW - Hadamard product

KW - Subordination

UR - http://www.scopus.com/inward/record.url?scp=67649544309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649544309&partnerID=8YFLogxK

M3 - Article

VL - 10

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

SN - 1443-5756

IS - 1

M1 - 8

ER -