Mathematics

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

Kumar Sanjay K., B. Rath, Krishna Vamshee D., Viswanadh Surya G. K.

Gandhi Institute of Technology and Management

Abstract: We obtain sharp bounds in the generalized Zalcman conjecture for the initial coefficients and the second Hankel determinants H2,1,k(f ), H2,2,k(f ) for the k^th-root transformation to the subclass of analytic functions.

Keywords: analytic function, univalent function, Hankel determinant, k^th-root trans- formation, Caratheodory function

UDC: 517.53

Received: 09.09.2023
Accepted: 29.02.2024

Language: English

DOI: 10.25587/2411-9326-2024-1-81-87