### Abstract

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f (z) = zh(z)g(z) defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, S ^{*}lh (A, B, α), with the functional z h (z) in the class of the generalized Janowski starlike functions, S * (A, B, α). By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, CST _{lh} (A, B, α).

Original language | English |
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Article number | 356915 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2011 |

DOIs | |

Publication status | Published - 2011 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**The generalized Janowski starlike and close-to-starlike log-harmonic mappings.** / Haji Mohd, Maisarah; Darus, Maslina.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - The generalized Janowski starlike and close-to-starlike log-harmonic mappings

AU - Haji Mohd, Maisarah

AU - Darus, Maslina

PY - 2011

Y1 - 2011

N2 - Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f (z) = zh(z)g(z) defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, S *lh (A, B, α), with the functional z h (z) in the class of the generalized Janowski starlike functions, S * (A, B, α). By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, CST lh (A, B, α).

AB - Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f (z) = zh(z)g(z) defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, S *lh (A, B, α), with the functional z h (z) in the class of the generalized Janowski starlike functions, S * (A, B, α). By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, CST lh (A, B, α).

UR - http://www.scopus.com/inward/record.url?scp=84855174125&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855174125&partnerID=8YFLogxK

U2 - 10.1155/2011/356915

DO - 10.1155/2011/356915

M3 - Article

AN - SCOPUS:84855174125

VL - 2011

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 356915

ER -