Coefficient Problems for Subclasses of Close-to-Star Functions

In this paper, two subclasses of close-to-star functions and two subclasses of close-to-convex functions are studied. By using the coefficient estimates of the known Carathéodory function classes, the upper bounds of the Zalcman functional J3,4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{3,4}$$\end{document}, Hankel determinant H2(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{H}_{2}}(3)$$\end{document} and Toeplitz determinant of given function classes are estimated. Some sharp results are obtained.