Hankel determinants of logarithmic coefficients for a class of bounded turning functions associated with Bell numbers

In this thesis, a new subclass of bounded turning functions whose coefficients are subordinate to the function whose coefficients are Bell numbers is defined and some initial logarithmic and inverse logarithmic coefficient bounds of the functions beloging to this subclass are obtained. Using these coefficients, exact bounds for the second Hankel determinant of the logarithmic coefficients H_2,1 (F_f⁄2) and the second Hankel determinant of the inverse logarithmic coefficients H_2,1 (F_(f^(-1) )⁄2) of bounded turning functions associated with Bell numbers are determined. Moreover, bounds for the third Hankel determinant of the logarithmic coefficients H_3,1 (F_f⁄2) and the third Hankel determinant of the inverse logarithmic coefficients H_3,1 (F_(f^(-1) )⁄2) of functions belonging to this new class are calculated. To enhance the clarity of the results, the thesis first presents the definitions and theorems underlying the theory of complex functions, followed by the definitions and theorems underlying the theory of univalent functions, and introduces some important subclasses. Additionally, the thesis provides information about the Hankel determinant and Bell numbers to facilitate understanding of the defined class and the obtained results.