Coefficient Problems of Starlike Functions Related to a Balloon-Shaped Domain

Abstract

Recent advances in image and signal processing have drawn on geometric function theory, particularly coefficient estimate problems. Motivated by their significance, we introduce a class of starlike functions related to a balloon-shaped domain

$$\mathcal {S}^{*}_{B}= \left\{ f \in \mathcal {A}: \frac{z f'(z)}{f(z)} \prec \frac{1}{1-\log (1+z)}:= B(z); \; z \in \mathbb {D} \right\} , $$

where \(B(z)\) maps the unit disk \(\mathbb {D}\) onto a balloon-shaped domain. This work establishes bounds for the second order Hankel determinants and second order Toeplitz determinants involving the initial coefficients, the logarithmic coefficients and the logarithmic coefficients of the inverse function for \(f \in \mathcal {S}^{*}_{B}.\)