Coefficient Estimates for the Class <span class="math-tex">\( \mathcal CL \)

<jats:p>In this paper, we study coefficient problems in some subclasses of convex functions. More precisely, we determine the upper bounds of initial coefficients \( |a_i|(2\leq i\leq 6) \), Zalcman inequalities, the second and third Hankel determinants, the second-order Hankel determinant of logarithmic coefficients and the third Hankel determinant of inverse functions for the class \( \mathcal CL \). All of the bounds are sharp.</jats:p>