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

Abstract

Starlike and convex functions have gained increased prominence in both academic literature and practical applications over the past decade. Concurrently, logarithmic coefficients play a pivotal role in estimating diverse properties within the realm of analytic functions, whether they are univalent or nonunivalent. In this paper, we rigorously derive bounds for specific Toeplitz determinants involving logarithmic coefficients pertaining to classes of convex and starlike functions concerning symmetric points. Furthermore, we present illustrative examples showcasing the sharpness of these established bounds. Our findings represent a substantial contribution to the advancement of our understanding of logarithmic coefficients and their profound implications across diverse mathematical contexts.

Keywords

• univalent functions
• starlike and convex functions
• symmetric points
• logarithmic coefficients
• Schwarz functions
• Toeplitz determinants