Hankel and Inverse-Coefficient Bounds for Functions with Bounded Turning

Abstract

In this paper, we investigate coefficient problems for the class of analytic functions with bounded turning, defined by the condition in the open unit disk. The study is based on the representation of the derivative of a normalized analytic function through the Carathéodory class of functions with positive real part. By employing classical coefficient inequalities and suitable coefficient-functional estimates, we derive bounds for the initial Taylor coefficients and investigate the corresponding inverse coefficients. Furthermore, we examine Hankel determinants.