Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function
Abstract
In this paper, we study a Ma--Minda type subclass of starlike functions associated with the normalized arcsine function φ(z)=1+2/πarcsin z. Using the Carathéodory function approach together with sharp coefficient estimates for Schwarz functions, we obtain explicit sharp bounds for the initial Taylor coefficients and logarithmic coefficients of functions in this class. We also derive a sharp estimate for the second Hankel determinant H2,2(f), as well as for the Hankel determinants H2,1(Ff/2) and H2,1(Ff−1/2) associated with the logarithmic coefficients of a function and its inverse. In addition, we establish a sharp bound for a difference involving logarithmic coefficients. The extremal functions for all the main results are identified, confirming the sharpness of the estimates.
Related
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BibTeX
@misc{panja2026coefficient,
title = {{Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function}},
author = {Shantanu Panja and Abhijit Banerjee and Sujoy Majumder},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20288},
eprint = {2609.20288},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20288},
}
RIS
TY - UNPB
TI - Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function
AU - Shantanu Panja
AU - Abhijit Banerjee
AU - Sujoy Majumder
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20288
UR - https://arxiv.org/abs/2609.20288
AB - In this paper, we study a Ma--Minda type subclass of starlike functions associated with the normalized arcsine function φ(z)=1+2/πarcsin z. Using the Carathéodory function approach together with sharp coefficient estimates for Schwarz functions, we obtain explicit sharp bounds for the initial Taylor coefficients and logarithmic coefficients of functions in this class. We also derive a sharp estimate for the second Hankel determinant H_2,2(f), as well as for the Hankel determinants H_2,1(F_f/2) and H_2,1(F_f^−1/2) associated with the logarithmic coefficients of a function and its inverse. In addition, we establish a sharp bound for a difference involving logarithmic coefficients. The extremal functions for all the main results are identified, confirming the sharpness of the estimates.
ER -