Toeplitz Determinants of Bi-Starlike and Bi-Convex Functions of Order ???? and their geometric behavior

Abstract

A regular function  defined in Ֆ:  is said to be univalent in Ֆ, if it assumes no value more than once in it. But  becomes Bi-univalent function in Ֆ if  and its inverse are univalent in Ֆ. These Bi-univalent functions are of great interest in recent research of Geometric Function Theory. The main focus of this work is to bring out the upper bound of the symmetric Toeplitz determinants  and   for the classes ????_????*(????) and ????_????(????). The novelty of this work lies in analyzing their geometric behavior. MSC 2020:  Primary 30C45, Secondary 11C20