Estimates of Toeplitz determinants for certain subclasses of bi-univalent function related to modified sigmoid function

Abstract

The current comprehensive study aimed to determine upper bounds of Toeplitz determinants for some subclasses of bi-univalent functions. A function f ∈ A is said to be bi-univalent in ∆ if both f and f−1 are univalent in ∆. Modified sigmoid function play an important role in Geometric function theory and in this paper we derive the Sharp coefficient estimates, Fekete-Szegö inequality, second and third order Toeplitz determinants, for the subclasses S*σ(S), Cσ(S) of bi-univalent Sakaguchi type functions associated with the modified sigmoid function.