The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

Abstract EN

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, Slh*(A,B,α), with the functional zh(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, CSTlh(A,B,α).