Toeplitz Determinant whose Its Entries are the Coefficients
for Class of Non-Bazilevi´c Functions
1Saba N. Al-khafaji, 2Ali Al-Fayadh, 3Ahmed Hadi Hussain, 4Sameer Annon
Abbas
1Department of Mathematics, Faculty of Computer Science and Mathematics,
University of Kufa.
2Department of Mathematics and Computer Applications, Al-Nahrain University-Iraq
3University of Babylon, College of Engineering Al-musayab, Department of Energy
Engineering
4Iraqi Ministry of Education, The Directorate of Education of the Governorate
Babylon

Abstract. The famous Toeplitz matrix is a matrix in which each descending diagonals form left
to right is constant, this mean  = 
  ? 
   … …
? ? ? ?
… ?   
.Mathematician, engineers, and
physicists are interested into this matrix for their computational properties and appearances in
various areas:
?-dynamical systems [1], dynamical systems [6], operator algebra [2],
Pseudospectrum and signal processing [10]. The object of this research is to define a new class
Non-Bazilevi´c functions  in unit disk  = { ? ?: || < 1} related to exponential function.
As well as, we obtained coefficient estimates and an upper bound for the second and third
determinant of the Toeplitz matrix such that the entries these matrix are belong to this class.