The sharp bound of the generalized Zalcman conjecture for initial coefficient and the certain second Hankel determinants of kth-root transformation for a subclass of analytic functions

Abstract

We obtain sharp bounds in the generalized Zalcman conjecture for the initial coefficients and the second Hankel determinants H_2,1,k(f ), H_2,2,k(f ) for the k^th-root transformation to the subclass of analytic functions.