Logarithmic coefficients for exponential classes of starlike and convex functions
Abstract
In this paper, we investigate two subclasses of univalent functions associated with the exponential mapping φ(z)=eαz, 0<α≤1, defined via the subordination conditions zf'(z)/f(z)≺ eαz and 1+zf''(z)/f'(z)≺ eαz. These classes provide a natural exponential analogue of several classical subclasses arising in geometric function theory. We obtain sharp coefficient estimates, logarithmic coefficient inequalities and sharp bounds for the associated Hankel determinants. In particular, explicit estimates are derived for H2,1(Ff/2) for functions belonging to the exponential subclasses introduced above of starlike and convex functions. Our results extend and unify several earlier works on exponential subclasses and highlight connections with logarithmic coefficients and determinant functionals.
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BibTeX
@misc{panja2026logarithmic,
title = {{Logarithmic coefficients for exponential classes of starlike and convex functions}},
author = {Shantanu Panja and Sujoy Majumder and Abhijit Banerjee and Janusz Sokół},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.29026},
eprint = {2605.29026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29026},
}
RIS
TY - UNPB
TI - Logarithmic coefficients for exponential classes of starlike and convex functions
AU - Shantanu Panja
AU - Sujoy Majumder
AU - Abhijit Banerjee
AU - Janusz Sokół
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2605.29026
UR - https://arxiv.org/abs/2605.29026
AB - In this paper, we investigate two subclasses of univalent functions associated with the exponential mapping φ(z)=e^αz, 0<α≤1, defined via the subordination conditions zf'(z)/f(z)≺ e^αz and 1+zf''(z)/f'(z)≺ e^αz. These classes provide a natural exponential analogue of several classical subclasses arising in geometric function theory. We obtain sharp coefficient estimates, logarithmic coefficient inequalities and sharp bounds for the associated Hankel determinants. In particular, explicit estimates are derived for H_2,1(F_f/2) for functions belonging to the exponential subclasses introduced above of starlike and convex functions. Our results extend and unify several earlier works on exponential subclasses and highlight connections with logarithmic coefficients and determinant functionals.
ER -