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

Abstract

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

Keywords

• Analytic function
• Subordination
• Majorization
• Exponential function
• Liu–Owa integral operator