### Abstract

The authors in [1] have recently introduced a new generalised derivatives operator μ ^{n,m} _{λ1, λ1}, which generalised many well-known operators studied earlier bymany different authors. By making use of the generalised derivative operator μ ^{n,m} _{λ1, λ1}, the authors derive the class of function denoted by H ^{n,m} _{λ1, λ1}, which contain normalised analytic univalent functions f defined on the open unit disc U = {z ε C : |z| < 1} and satisfy Re(μ ^{n,m} _{λ1, λ1} f (z))' > 0, (z ε U). This paper focuses on attaining sharp upper bound for the functional |a _{2}a _{4} - a ^{2} _{3}| for functions f (z)= {equation presented} belonging to the class H ^{n,m} _{λ1, λ1}.

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

Pages (from-to) | 445-453 |

Number of pages | 9 |

Journal | Tamkang Journal of Mathematics |

Volume | 43 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2012 |

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### Keywords

- Analytic function
- Convex and starlike functions
- Derivative operator
- Fekete-Szegö functional
- Hankel determinant
- Positive real functions
- Univalent function

### ASJC Scopus subject areas

- Metals and Alloys
- Materials Science(all)

### Cite this

**Hankel determinant for certain class of analytic function defined by generalised derivative operator.** / Al-Abbadi, Ma'Moun Harayzeh; Darus, Maslina.

Research output: Contribution to journal › Article

*Tamkang Journal of Mathematics*, vol. 43, no. 3, pp. 445-453. https://doi.org/10.5556/j.tkjm.43.2012.445-453

}

TY - JOUR

T1 - Hankel determinant for certain class of analytic function defined by generalised derivative operator

AU - Al-Abbadi, Ma'Moun Harayzeh

AU - Darus, Maslina

PY - 2012/9

Y1 - 2012/9

N2 - The authors in [1] have recently introduced a new generalised derivatives operator μ n,m λ1, λ1, which generalised many well-known operators studied earlier bymany different authors. By making use of the generalised derivative operator μ n,m λ1, λ1, the authors derive the class of function denoted by H n,m λ1, λ1, which contain normalised analytic univalent functions f defined on the open unit disc U = {z ε C : |z| < 1} and satisfy Re(μ n,m λ1, λ1 f (z))' > 0, (z ε U). This paper focuses on attaining sharp upper bound for the functional |a 2a 4 - a 2 3| for functions f (z)= {equation presented} belonging to the class H n,m λ1, λ1.

AB - The authors in [1] have recently introduced a new generalised derivatives operator μ n,m λ1, λ1, which generalised many well-known operators studied earlier bymany different authors. By making use of the generalised derivative operator μ n,m λ1, λ1, the authors derive the class of function denoted by H n,m λ1, λ1, which contain normalised analytic univalent functions f defined on the open unit disc U = {z ε C : |z| < 1} and satisfy Re(μ n,m λ1, λ1 f (z))' > 0, (z ε U). This paper focuses on attaining sharp upper bound for the functional |a 2a 4 - a 2 3| for functions f (z)= {equation presented} belonging to the class H n,m λ1, λ1.

KW - Analytic function

KW - Convex and starlike functions

KW - Derivative operator

KW - Fekete-Szegö functional

KW - Hankel determinant

KW - Positive real functions

KW - Univalent function

UR - http://www.scopus.com/inward/record.url?scp=84867219068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867219068&partnerID=8YFLogxK

U2 - 10.5556/j.tkjm.43.2012.445-453

DO - 10.5556/j.tkjm.43.2012.445-453

M3 - Article

AN - SCOPUS:84867219068

VL - 43

SP - 445

EP - 453

JO - Tamkang Journal of Mathematics

JF - Tamkang Journal of Mathematics

SN - 0049-2930

IS - 3

ER -