The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions

Abstract

The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f′(0) = 1 in the open unit disk D := {z ∈ C : |z| < 1}.