ESTIMATES OF TOEPLITZ DETERMINANTS FOR CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTION RELATED TO MODIFIED SIGMOID FUNCTION

ESTIMATES OF TOEPLITZ DETERMINANTS FOR CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTION RELATED TO MODIFIED SIGMOID FUNCTION

S. P. Vijayalakshmi, J. Sree Rithika

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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 Δ if both f and f−1 are univalent in Δ. Modified sigmoid function play an important role in Geometric function theory and in this paper we derive the Sharp coefficient estimates, Fekete-Szeg¨o 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.

Keywords

Sakaguchi functions, Toeplitz determinants, modified sigmoid function, starlike functions, convex function.