Symmetric Toeplitz determinants for classes defined by post quantum operators subordinated to the limaçon function

Sangarambadi Padmanabhan Vijayalakshmi, Thirumalai Vinjimur Sudharsan, Teodor Bulboacă

Abstract


The present extensive study is focused to find estimates for the upper bounds of the Toeplitz determinants. The logarithmic coefficients of univalent functions play an important role in different estimates in the theory of univalent functions, and in the this paper we derive the estimates of Toeplitz determinants and Toeplitz determinants of the logarithmic coefficients for the subclasses \(\mathrm{L}_{s}\mathcal{S}_p^q\) and \(\mathrm{L}_{s}\mathcal{C}_p^q\), \(0<q\leq p\leq1\), defined by post quantum operators, which map the open unit disc \(\mathbb{D}\) onto the domain bounded by the limaçon curve defined by \(\partial\mathcal{D}_{s}:=\left\{u+iv\in\mathbb{C}:\left[(u-1)^{2}+v^{2}-s^{4}\right]^{2}=4s^{2}\left[(u-1+s^{2})^{2}+v^{2}\right]\right\}\), where \(s\in[-1,1]\setminus\{0\}\).


Keywords


Limaçon domain; subordination; Toeplitz and Hankel determinants; symmetric Toeplitz determinant; logarithmic coefficients; starlike functions with respect to symmetric points

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.2.04

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