### Abstract

For α ≥ 0, we introduce the class M^{α} of normalised analytic α-logarithmically convex functions defined in the open unit disc D by Re{(1 +zf″ (z)/f′ (z))^{α} (zf′ (z)/f(z))^{1-α} } > 0 For f ∈ M^{α}, a best possible subordination theorem is obtained which implies that M^{α} forms a subset of the starlike functions S*. Some extreme coefficient problems are also solved.

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

Pages (from-to) | 1049-1059 |

Number of pages | 11 |

Journal | Indian Journal of Pure and Applied Mathematics |

Volume | 29 |

Issue number | 10 |

Publication status | Published - Oct 1998 |

Externally published | Yes |

### Fingerprint

### Keywords

- α-logarithm
- Convex functions
- Extreme coefficient problem
- Fekete-Szegö functional

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indian Journal of Pure and Applied Mathematics*,

*29*(10), 1049-1059.

**α-Logarithmically convex functions.** / Darus, Maslina; Thomas, D. K.

Research output: Contribution to journal › Article

*Indian Journal of Pure and Applied Mathematics*, vol. 29, no. 10, pp. 1049-1059.

}

TY - JOUR

T1 - α-Logarithmically convex functions

AU - Darus, Maslina

AU - Thomas, D. K.

PY - 1998/10

Y1 - 1998/10

N2 - For α ≥ 0, we introduce the class Mα of normalised analytic α-logarithmically convex functions defined in the open unit disc D by Re{(1 +zf″ (z)/f′ (z))α (zf′ (z)/f(z))1-α } > 0 For f ∈ Mα, a best possible subordination theorem is obtained which implies that Mα forms a subset of the starlike functions S*. Some extreme coefficient problems are also solved.

AB - For α ≥ 0, we introduce the class Mα of normalised analytic α-logarithmically convex functions defined in the open unit disc D by Re{(1 +zf″ (z)/f′ (z))α (zf′ (z)/f(z))1-α } > 0 For f ∈ Mα, a best possible subordination theorem is obtained which implies that Mα forms a subset of the starlike functions S*. Some extreme coefficient problems are also solved.

KW - α-logarithm

KW - Convex functions

KW - Extreme coefficient problem

KW - Fekete-Szegö functional

UR - http://www.scopus.com/inward/record.url?scp=0032193652&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032193652&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032193652

VL - 29

SP - 1049

EP - 1059

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

SN - 0019-5588

IS - 10

ER -