• 호남수학학술지
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• 제43권3호
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• pp.465-481
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• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• 대한수학회보
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• 제60권2호
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• 대한수학회보
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• 제61권2호
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• pp.317-333
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• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• 대한수학회논문집
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• 제39권3호
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• pp.647-655
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• 2024

In this article, by making use of the λ-pseudo-starlike functions, we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T₂(2), T₂(3), T₃(2) and T₃(1) for the functions belonging to this family. Further, some known and new results which follow as special cases of our results are also mentioned.

• 대한수학회논문집
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• 제37권4호
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.429-438
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• 2015

The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $k^{th}$ root transform $[f(z^k)]^{\frac{1}{k}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.

• Kyungpook Mathematical Journal
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• 제54권3호
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• pp.443-452
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• 2014

In the present investigation we consider Fekete-Szeg$\ddot{o}$ problem with complex parameter ${\mu}$ and also find upper bound of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for functions belonging to a new class $S^{\tau}_{\gamma}(A,B)$ using Toeplitz determinants.

• 대한수학회지
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• 제59권5호
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• pp.997-1013
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• 2022

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some 4 × 4 and 6 × 6 Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.