Some Results for Certain Subclasses of Functions with Differential Equation and Subordination

Liangpeng Xiong, Xiaoli Liu

Abstract

By applying the differential subordination theorem, we further investigate the subclassHn, [,] of functions which are analytic in the unit disk. Several subordination results on a convex function and a incomplete beta function are obtained. Moreover, the function that belongs to the Hn, [,] with a Cauchy-Euler differential equation is also discussed on similar subject. Our results extend some earlier works.

Keywords

Analytic functions, Convex function, Subordination, Differential equation

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