Majorization problems for two subclasses of analytic functions connected with the Liua??Owa integral operator and exponential function

摘要

In the present paper, we investigate majorization properties for the class (M_{eta}^{lpha}(p,gamma)) of uniformly starlike functions and the class (N_{eta}^{lpha}(p,heta)) of spiral-like functions related to an exponential function, which are defined through the Liua??Owa integral operator (Q_{eta,p}^{lpha}) given by (1.5). Also, some special cases of our main results in a form of corollaries are shown.