Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and exponential function.

Abstract

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