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

Huo Tang; Guantie Deng

doi:10.1186/s13660-018-1865-x

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

J Inequal Appl. 2018;2018(1):277. doi: 10.1186/s13660-018-1865-x. Epub 2018 Oct 11.

Authors

Huo Tang¹, Guantie Deng²

Affiliations

¹ 1School of Mathematics and Statistics, Chifeng University, Chifeng, People's Republic of China.
² 2School of Mathematical Sciences, Beijing Normal University, Beijing, People's Republic of China.

Abstract

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

Keywords: Analytic function; Exponential function; Liu–Owa integral operator; Majorization; Subordination.