The famous Toeplitz matrix is a matrix in which each descending diagonals form left to right is constant, this mean T = ( a 0 a 1 ⋯ a n a − 1 a 0 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ ⋯ ⋯ a − 1 a 0 ) . Mathematician, engineers, and physicists are interested into this matrix for their computational properties and appearances in various areas: C *-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 N δ in unit disk ↁ = {z ∈ ℂ: |z| < 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.
The aim of this paper is to clarify several important points, including a brief and adequate explanation of loving improvement, as well as laying out a number of important mathematical formulas that we need, supported with graphs.
In many branches of pure analysis, Integral Equations are one of the most useful techniques, such as functional analysis theories and stochastic processes. It is one of the most significant branches of mathematical analysis, in many fields of mechanics and mathematical physics,. In this research, we will address the integral equations in many physical issues and their applications. They are also associated with mechanical vibration problems, analytic function theory, orthogonal systems, quadratic form theory of infinitely many variables.
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