Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

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 Ls𝑆𝑝𝑞 L𝑠C𝑝𝑞 and LsS𝑝𝑞 ∩ S, L𝑠𝐶𝑝𝑞 ∩ S, 0 q≤p≤10 𝑞≤𝑝≤1, defined by post quantum operators, which map the open unit disc 𝐷 onto the domain bounded by the limaçon curve defined by ∂Ds:={u+iv∈C:(u−1)2+v2−s4.2=4s2(u−1+s2)2+v2.}, where s∈−1,1.∖{0}. Keywords: Limaçon domain, subordination, (p, q)–derivative, Toeplitz and Hankel determinants, symmetric Toeplitz determinant, logarithmic coefficients, starlike functions with respect to symmetric points.