Sharp coefficient problems of functions with bounded turning subordinated to the domain of cosine hyperbolic function

Abstract

In the current article, we consider a class of bounded turning functions associated with the cosine hyperbolic function and give some results containing coefficient functionals using the familiar Carathéodory functions. An improvement on the bound of the third-order Hankel determinant for functions in this class is provided. Furthermore, we obtain sharp estimates of the Fekete-Szegö, Krushkal, and Zalcman functionals with logarithmic coefficients as entries. All the findings are proved to be sharp.

Keywords

• hankel determinant
• bounded turning functions
• cosine hyperbolic function
• logarithmic coefficient problems