English

Second Hankel determinant of Logarithmic coefficients for Starlike and Convex functions associated with lune

Complex Variables 2023-07-07 v1

Abstract

The Hankel determinant H2,1(Ff/2)H_{2,1}(F_{f}/2) is defined as: \begin{align*} H_{2,1}(F_{f}/2):= \begin{vmatrix} \gamma_1 & \gamma_2 \gamma_2 & \gamma_3 \end{vmatrix}, \end{align*} where γ1,γ2,\gamma_1, \gamma_2, and γ3\gamma_3 are the first, second and third logarithmic coefficients of functions belonging to the class S\mathcal{S} of normalized univalent functions. In this article, we establish sharp inequalities H2,1(Ff/2)1/16|H_{2,1}(F_{f}/2)|\leq 1/16 and H2,1(Ff/2)23/3264|H_{2,1}(F_{f}/2)| \leq 23/3264 for the logarithmic coefficients of starlike and convex functions associated with lune.

Keywords

Cite

@article{arxiv.2307.02741,
  title  = {Second Hankel determinant of Logarithmic coefficients for Starlike and Convex functions associated with lune},
  author = {Sanju Mandal and Molla Basir Ahamed},
  journal= {arXiv preprint arXiv:2307.02741},
  year   = {2023}
}