• Title/Summary/Keyword: Hermitian-Toeplitz determinant

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THE THIRD HERMITIAN-TOEPLITZ AND HANKEL DETERMINANTS FOR PARABOLIC STARLIKE FUNCTIONS

  • Rosihan M. Ali;Sushil Kumar;Vaithiyanathan Ravichandran
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.2
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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.

SHARP ESTIMATES ON THE THIRD ORDER HERMITIAN-TOEPLITZ DETERMINANT FOR SAKAGUCHI CLASSES

  • Kumar, Sushil;Kumar, Virendra
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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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.

SHARP BOUNDS OF FIFTH COEFFICIENT AND HERMITIAN-TOEPLITZ DETERMINANTS FOR SAKAGUCHI CLASSES

  • Surya Giri;S. Sivaprasad Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.2
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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 Cs(𝜑), respectively, the sharp bound of the nth 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.