Fourth Toeplitz Determinants for Starlike Functions Defined by Using the Sine Function

Abstract

In this article, we aim to study the upper bounds of the fourth Toeplitz determinant T 4 2 for the function class S s ∗ , which are connected with the sine function.

Toeplitz Determinant for the Inverse of a Function Whose Derivative Has a Positive Real Part

“…Since 𝑓(𝑧) ∈ 𝑅, there exists a function 𝑝(𝑧) = 1 + ∑ ∞ 𝑛=1 𝑐 𝑛 𝑧 𝑛 ∈ 𝑃, such that 𝑓 ′ (𝑧) = 𝑝(𝑧). Comparing the coefficients of 𝑧, 𝑧 2 , 𝑧 3 , 𝑧 4 , we obtain…”

Toeplitz Determinants for a Certain Family of Analytic Functions Endowed with Borel Distribution

“…The notion of Toeplitz matrices acts a significant part in applied mathematics, functional analysis as well as in physics and technical sciences (for more details, see [9]). Very recently, several authors established estimates of the Toeplitz determinant T q (n) for functions belonging to various classes of univalent functions (see, for example, [10][11][12][13][14][15][16][17][18][19][20][21]). In order to obtain wanted bounds in our study, we need the lemmas given below.…”