Refereed journal article or data article (A1)

Notes on the starlike log-harmonic mappings of order alpha




List of Authors: Rahim Kargar, Hesam Mahzoon

Publisher: Springer

Publication year: 2020

Journal: Boletín de la Sociedad Matemática Mexicana

Volume number: 26

Issue number: 2

Number of pages: 10

ISSN: 1405-213X

DOI: http://dx.doi.org/10.1007/s40590-019-00249-z

URL: https://link.springer.com/article/10.1007/s40590-019-00249-z


Abstract

Let h and g be two analytic functions in the unit disc Δ Δ that g (0)= 1 g (0)= 1. Also let β β be a complex number with Re {β\}>-1/2 Re β>-1/2. A function f is said to be log-harmonic mapping if it has the following representation: f (z)= z| z|^ 2 β h (z) g (z)\quad (z ∈ Δ). f (z)= z| z| 2 β h (z) g (z)¯(z∈ Δ). A log-harmonic mapping f is said to be starlike log-harmonic mapping of order α α, where 0 ≤ α< 1 0≤ α< 1, if Re\left {zf_z-z f_ z f\right\}> α\quad (z ∈ Δ). Re zfz-z¯ fz¯ f> α (z∈ Δ). In this paper, by use of the subordination principle, we study some geometric properties of the starlike log-harmonic mappings of order α α. Also, we estimate the Jacobian of log-harmonic mappings.


Last updated on 2021-24-06 at 10:02