Sharp bounds on the Hankel determinant of the inverse functions for certain analytic functions

In most cases, the problem of finding bounds for the inverse function is much more difficult than finding bounds for the function itself.Thus, there are relatively little sharp bounds of Hankel determinant on the inverse functions.In the present paper, we introduce a subclass of bounded turning function R car associated with a cardioid domain.The purpose of this article is to investigate certain coefficient related problems on the inverse functions for f R car .The bounds of some initial coefficients, the Fekete-Szeg type inequality and the estimation of Hankel determinants of second and third order are obtained.All of these bounds are proved to be sharp.