Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function

Muhammad Ghaffar Khan, Bakhtiar Ahmad, Janusz Sokol, Zubair Muhammad, Wali Khan Mashwani, Ronnason Chinram, Pattarawan Petchkaew

Abstract

The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.

Keywords

Holomorphic functions, Subordinations, Trigonometric function, Hankel determinant

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