### Abstract

In this paper, a differential operator A_{λ}
^{n}
_{P}(α, β, μ) f(z) defined in the open unit disc U ={z ∈ ℂ : |z| <1} is introduced. We then, using this operator, introduce a new subclass of analytic functions G^{p}
_{n} (α, β, μ, λ, γ, δ). Moreover, we discuss radii of close-to-convexity, starlikeness and convexity. Furthermore, we give an application involving fractional calculus for functions in G^{p}
_{n} (α, β, μ, λ, γ, δ).

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

Pages (from-to) | 75-87 |

Number of pages | 13 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 99 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

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### Keywords

- Analytic functions
- Differential operator
- Fractional calculus
- p-valent functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Far East Journal of Mathematical Sciences*,

*99*(1), 75-87. https://doi.org/10.17654/MS099010075

**A certain fractional derivative operator for p-valent functions and new class of analytic functions with negative coefficients.** / Amourah, A. A.; Yousef, Feras; Al-Hawary, Tariq; Darus, Maslina.

Research output: Contribution to journal › Article

*Far East Journal of Mathematical Sciences*, vol. 99, no. 1, pp. 75-87. https://doi.org/10.17654/MS099010075

}

TY - JOUR

T1 - A certain fractional derivative operator for p-valent functions and new class of analytic functions with negative coefficients

AU - Amourah, A. A.

AU - Yousef, Feras

AU - Al-Hawary, Tariq

AU - Darus, Maslina

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper, a differential operator Aλ n P(α, β, μ) f(z) defined in the open unit disc U ={z ∈ ℂ : |z| <1} is introduced. We then, using this operator, introduce a new subclass of analytic functions Gp n (α, β, μ, λ, γ, δ). Moreover, we discuss radii of close-to-convexity, starlikeness and convexity. Furthermore, we give an application involving fractional calculus for functions in Gp n (α, β, μ, λ, γ, δ).

AB - In this paper, a differential operator Aλ n P(α, β, μ) f(z) defined in the open unit disc U ={z ∈ ℂ : |z| <1} is introduced. We then, using this operator, introduce a new subclass of analytic functions Gp n (α, β, μ, λ, γ, δ). Moreover, we discuss radii of close-to-convexity, starlikeness and convexity. Furthermore, we give an application involving fractional calculus for functions in Gp n (α, β, μ, λ, γ, δ).

KW - Analytic functions

KW - Differential operator

KW - Fractional calculus

KW - p-valent functions

UR - http://www.scopus.com/inward/record.url?scp=84951311174&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951311174&partnerID=8YFLogxK

U2 - 10.17654/MS099010075

DO - 10.17654/MS099010075

M3 - Article

AN - SCOPUS:84951311174

VL - 99

SP - 75

EP - 87

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 1

ER -