Some Analysis of the Coefficient-Related Problems for Functions of Bounded Turning Associated with a Symmetric Image Domain

Abstract

In the last few years, numerous subfamilies of univalent functions, whether directly or indirectly associated with exponential functions, have been introduced and thoroughly investigated. Among these, the families Se*, Ce and Re defined by subordination to ez have been intensively investigated. While the coefficient problem on the class Se* and Ce has been solved in many cases, in this paper, we mainly intend to compute the sharp estimates of some initial coefficients, the Feketo–Szegö inequality, and the sharp bounds of second- and third-order Hankel determinants for functions belonging to the class Re. This work has the potential to significantly enrich and enhance the exploration of univalent functions in conjunction with exponential functions, making the field more comprehensive and robust.

Keywords

• Hankel determinant
• bounded turning functions
• exponential function