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

Authors

DOI:

https://doi.org/10.12697/ACUTM.2023.27.15

Keywords:

univalent function, Hankel determinant, bounded turning functions, kth-root transformation, Caratheodory function

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}.

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Author Biographies

H. M. SRIVASTAVA

Department of Mathematics and Statistics, University of Victoria, Canada;

Department of Medical Research, China Medical University, Taiwan;

Center for Converging Humanities, Kyung Hee University, Republic of Korea;

Department of Mathematics and Informatics, Azerbaijan University, Azerbaijan;

Section of Mathematics, International Telematic University Uninettuno, Italy;

Department of Applied Mathematics, Chung Yuan Christian University, Taiwan.

Biswajit Rath, GITAM University

Department of Mathematics

K. SANJAY KUMAR, GITAM University

Department of Mathematics

D. VAMSHEE KRISHNA, North-Eastern Hill University

Department of Mathematics

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Published

2023-12-01

Issue

Vol. 27 No. 2 (2023)

Section

Articles