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

摘要

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the formf(z)=zh(z)g(z)¯defined on the open unit discU. The functions are in the class of the generalized Janowski starlike log-harmonic mapping,Slh*(A,B,α), with the functionalzh(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).