### Abstract

In the present investigation, sharp upper bounds of a3-αa_{2}
^{2} for functions f(z) = z+a_{2}
^{z2} + a_{3}
^{z3}+... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

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

Journal | Australian Journal of Mathematical Analysis and Applications |

Volume | 5 |

Issue number | 2 |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- Analytic functions
- Coefficient problem
- Convex functions
- Fekete-Szegö inequality
- k-symmetric points
- Starlike functions
- Subordination

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Fekete-Szegö problem for univalent functions with respect to k-symmetric points.** / Al-Shaqsi, K.; Darus, Maslina.

Research output: Contribution to journal › Article

*Australian Journal of Mathematical Analysis and Applications*, vol. 5, no. 2.

}

TY - JOUR

T1 - Fekete-Szegö problem for univalent functions with respect to k-symmetric points

AU - Al-Shaqsi, K.

AU - Darus, Maslina

PY - 2008

Y1 - 2008

N2 - In the present investigation, sharp upper bounds of a3-αa2 2 for functions f(z) = z+a2 z2 + a3 z3+... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

AB - In the present investigation, sharp upper bounds of a3-αa2 2 for functions f(z) = z+a2 z2 + a3 z3+... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

KW - Analytic functions

KW - Coefficient problem

KW - Convex functions

KW - Fekete-Szegö inequality

KW - k-symmetric points

KW - Starlike functions

KW - Subordination

UR - http://www.scopus.com/inward/record.url?scp=60149087123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60149087123&partnerID=8YFLogxK

M3 - Article

VL - 5

JO - Australian Journal of Mathematical Analysis and Applications

JF - Australian Journal of Mathematical Analysis and Applications

SN - 1449-5910

IS - 2

ER -