Premium
On rotationally starlike logharmonic mappings
Author(s) -
AbdulHadi Z.,
Ali Rosihan M.
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400056
Subject(s) - mathematics , class (philosophy) , distortion (music) , unit disk , order (exchange) , radius , unit (ring theory) , mathematical analysis , analytic function , pure mathematics , artificial intelligence , computer science , computer network , amplifier , mathematics education , computer security , bandwidth (computing) , finance , economics
This paper considers the class H G of all mappings of the form φ ( z ) = z h ( z ) g ( z ) , where h and g are analytic in the unit disk U , normalized by h ( 0 ) = g ( 0 ) = 1 , and such that f ( z ) = z h ( z )g ( z ) ¯is logharmonic with respect to an analytic self‐map a of U . A distortion estimate and the radius of starlikeness are obtained for this class. Additionally, a solution to the problem of minimizing the moments of order p over the class is found, as well as an estimate for arclength.