Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions

Hermitian Toeplitz determinants are used in multiple disciplines, including functional analysis, applied mathematics, physics, and engineering sciences. We calculate the sharp upper and lower bounds on the fourth-order Hermitian Toeplitz determinant for the subclass of bounded turning functions associated with the nephroid function represented by Rn. A nephroid function is associated with the geometric shape of a nephroid (a kidney-shaped curve) and refers to a specific type of epicycloid with two cusps. In geometric function theory, a bounded turning function is an analytic function whose derivative has a positive real part, ensuring that its tangent vector does not turn too sharply at any point.