Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions

Abstract

We define a class ${\tilde{T}}_k$ [$\mathrm{A,\; B}$, $\alpha$, $\rho$] of analytic functions by using Janowski’s functions which generalizes a number of classes studied earlier such as the class of strongly close-to-convex functions. Some properties of this class, including arc length, coefficient problems, and a distortion result, are investigated. We also discuss the growth of Hankel determinant problem.