Properties of some univalent functions associated with balloon-shaped domain

This paper introduces a novel subclass of analytic functions defined by the product of a modified sigmoid function and the lemniscate Bernoulli function. We initiate the study by deriving initial coefficient bounds for functions within this subclass, followed by an investigation into several key analytic properties. Specifically, we establish the Fekete–Szegö inequality and analyze Hankel determinants of various orders. Furthermore, the study provides estimates for the logarithmic coefficients and establishes bounds for both the inverse coefficients and the logarithmic inverse coefficients of functions in the subclass. This comprehensive analysis offers a significant contribution to the theory of analytic function subclasses associated with the products of special functions.