대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권2호
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  • Pages.317-333
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  • 2024
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SHARP BOUNDS OF FIFTH COEFFICIENT AND HERMITIAN-TOEPLITZ DETERMINANTS FOR SAKAGUCHI CLASSES

  • Surya Giri (Department of Applied Mathematics Delhi Technological University) ;
  • S. Sivaprasad Kumar (Department of Applied Mathematics Delhi Technological University)
  • 투고 : 2023.01.07
  • 심사 : 2024.01.08
  • 발행 : 2024.03.31
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초록

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.

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과제정보

The work of the Surya Giri is supported by University Grant Commission, New-Delhi, India under UGC-Ref. No. 1112/(CSIR-UGC NET JUNE 2019).

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