2024/12/23 by Surendra Kumar, Kumar, S. Sivaprasad, Tripathi, Arya +2
Mathematics · #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2412.17403
Logarithmic and inverse logarithmic coefficients play a crucial role in the theory of univalent functions. In this study, we focus on the class of starlike functions \(S^*ρ\), defined as S^*ρ= \ f ∈ A : (z f'(z))/(f(z)) \prec ρ(z), z ∈ \mathbbD \, where \(ρ(z) := 1 + \sinh-1(z)\), which maps the unit disk \(\mathbbD\) onto a petal-shaped domain. This investigation aims to establish bounds for the second Hankel and Toeplitz determinants, with their entries determined by the logarithmic coefficients of \(f\) and its inverse \(f-1\), for functions \(f ∈ S^*ρ\).