In this paper, we introduce a novel bounded subclass of analytic functions by the concept of subordination. This subclass is associated with a bean-shaped region that is symmetric about the real axis. Our primary focus is on derived sharp upper bounds for specific Hankel determinants and Toeplitz determinants. The second and third order Hankel determinants are denoted as \({\mathcal {H}}_{2,1}(f)\) , \({\mathcal {H}}_{2,2}(f)\) , and \({\mathcal {H}}_{3,1}(f)\) as well as the Toeplitz determinants as \({\mathcal {T}}_{2,2}(f)\) and \({\mathcal {T}}_{3,1}(f)\) respectively. These determinants are crucial in understanding the properties and behaviors of the functions within this newly defined class. By establishing these bounds, we make a significant contribution to the broader field of geometric function theory. The results have important implications for studying analytic functions and their various subclasses. This work not only enhances our understanding of these functions but also opens up new avenues for exploration in geometric function theory.
