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Some properties of a generalized class of analytic functions related with Janowski functions. (English) Zbl 1242.30009

Summary: We define a class \(\widetilde{T}_k [A, B, \alpha, \rho]\) 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.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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