The objective of this paper is to estimate the best possible upper bound to the third Hankel determinant for the inverse of functions with normalized conditions f (0) = 0, f ′(0) = 1 in the unit disc whose derivative has positive real part.

The objective of this paper is to estimate the sharp bound of thethird Hankel determinant for kth- root transformation to the familiar subfamilyof starlike functions associated with the right half of lemniscate of Bernoulli. 2020 Mathematics Subject Classification. 30C45, 30C50.