Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions

Abstract

In this article, we use the q-derivative operator and the principle of subordination to define a new subclass of analytic functions related to the q-Ruscheweyh operator. Sufficient conditions, sharp bounds for the initial coefficients, a Fekete–Szegö functional and a Toeplitz determinant are investigated for this new class of functions. Additionally, we also present several established consequences derived from our primary findings.

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

“…Recently, Mandal et al [17] determined the best possible bounds for second Hankel and Hermitian Toeplitz matrices, involving logarithmic coefficients of inverse functions, which are applied to starlike and convex functions concerning symmetric points. In recent studies, considerable attention has been devoted to exploring interesting properties associated with Teoplitz and Hankel determinants within the realm of analytic functions of certain classes of convex and starlike functions (see, for example, [18][19][20][21][22][23][24][25][26][27] and references therein). The Toeplitz determinant, characterized by entries corresponding to the logarithmic coefficients of g ∈ S in the form (14), is expressed as…”