### Abstract

Let A be the class of analytic functions in the open unit disk U = {z : z <1}. The sharp bound is obtained for the coefficient functional |a _{3} - μa_{2}
^{2}|, where μεC or and are respectively the second and the third coefficient for f belonging to a certain subclass R_{α,β(γ,ρ)} defined by a fractional operator. By specializing the parameters α,β,γ and ρ, many consequence results are obtained. Further, an improvement for the estimation of |a_{3} - μa_{2}
^{2}| is investigated by dividing the intervals of μ ε R. In addition, sharp estimates for the first few coefficients of the inverse functions of R _{α,β(γ,ρ)} are derived.

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

Pages (from-to) | 179-188 |

Number of pages | 10 |

Journal | Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science |

Volume | 12 |

Issue number | 3 |

Publication status | Published - Jul 2011 |

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### Keywords

- Coefficient inequality
- Fekete-Szegö inequality
- Fractional derivative
- Hankel determinant

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)
- Computer Science(all)

### Cite this

**On the fekete-szegö theorem for the generalized owa-srivastava operator.** / Ajwely, Aisha; Darus, Maslina.

Research output: Contribution to journal › Article

*Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science*, vol. 12, no. 3, pp. 179-188.

}

TY - JOUR

T1 - On the fekete-szegö theorem for the generalized owa-srivastava operator

AU - Ajwely, Aisha

AU - Darus, Maslina

PY - 2011/7

Y1 - 2011/7

N2 - Let A be the class of analytic functions in the open unit disk U = {z : z <1}. The sharp bound is obtained for the coefficient functional |a 3 - μa2 2|, where μεC or and are respectively the second and the third coefficient for f belonging to a certain subclass Rα,β(γ,ρ) defined by a fractional operator. By specializing the parameters α,β,γ and ρ, many consequence results are obtained. Further, an improvement for the estimation of |a3 - μa2 2| is investigated by dividing the intervals of μ ε R. In addition, sharp estimates for the first few coefficients of the inverse functions of R α,β(γ,ρ) are derived.

AB - Let A be the class of analytic functions in the open unit disk U = {z : z <1}. The sharp bound is obtained for the coefficient functional |a 3 - μa2 2|, where μεC or and are respectively the second and the third coefficient for f belonging to a certain subclass Rα,β(γ,ρ) defined by a fractional operator. By specializing the parameters α,β,γ and ρ, many consequence results are obtained. Further, an improvement for the estimation of |a3 - μa2 2| is investigated by dividing the intervals of μ ε R. In addition, sharp estimates for the first few coefficients of the inverse functions of R α,β(γ,ρ) are derived.

KW - Coefficient inequality

KW - Fekete-Szegö inequality

KW - Fractional derivative

KW - Hankel determinant

UR - http://www.scopus.com/inward/record.url?scp=84859080188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859080188&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84859080188

VL - 12

SP - 179

EP - 188

JO - Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science

JF - Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science

SN - 1454-9069

IS - 3

ER -