The sharp bound of certain second Hankel determinants for inverse functions of the class of convex functions with respect to symmetric points

In this paper, we focus on the sharp upper bounds for specific second-order Hankel determinants pertaining to the inverse function, denoted as f−1. Our investigation is centered on scenarios where f is a member of the class of convex functions with respect to symmetric points. By delving into this particular class, we aim to uncover and establish sharp bounds for these second Hankel determinants, providing valuable insights to extremal functions within this context.