English

On geometrical properties of logharmonic mappings

Complex Variables 2016-10-05 v1 Classical Analysis and ODEs Functional Analysis

Abstract

In this paper, we find the radius of the disk Ωr\Omega _{r} such that every starlike logharmonic mapping f(z)f(z) of order α,\alpha , is starlike in % |z|\leq r with respect to any point of Ωr.\Omega _{r}. We also establish a relation between the set of starlike logharmonic mappings \ and the set of starlike logharmonic mappings of order alpha. Moreover, the radius of starlikeness and univalence for the set of close to starlike logharmonic mappings of order α\alpha is determined.

Keywords

Cite

@article{arxiv.1610.01087,
  title  = {On geometrical properties of logharmonic mappings},
  author = {Zayid Abdulhadi and Layan El Hajj},
  journal= {arXiv preprint arXiv:1610.01087},
  year   = {2016}
}