Let $\mathcal{B}{T}_{4l}$ denote a subclass of bounded turning functions connected with a four-leaf-type domain. The goal of the study is to probe into the bounds of coefficients $|b_6|,|b_7|,|b_8|$, the bounds of the logarithmic coefficients, and the third-order determinants $|H_{3,1}|,|H_{3,2}|,|H_{3,3}|$ for the functions in this class.

Let ${\mathcal{R}}_{LP}$ denote a newly introduced subclass of bounded turning functions. The primary aim of this study is to investigate the sharp bounds of the coefficients of $|d_2|,|d_3|,|d_4|,|d_5|$, as well as to establish precise estimates for the second- and third-order Hankel determinants $H_{2,1},H_{2,2},H_{2,3}$, and $H_{3,1}$ for functions belonging to this class. The coefficient bounds and Hankel determinant estimates derived herein are all shown to be sharp.