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Dergiler / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 6

Hermitian–Toeplitz determinants for functions with bounded turning

Virendra KUMAR
Nak Eun CHO
Sayfa
2678–2687
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order α, are obtained.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory.
📊
Temel Bulgular & Veri:It is also, therefore, natural to explore the concept of the Hermitian–Toeplitz determinants for such functions.
💡
Sonuç & Katkı:In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order α, are obtained.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian–Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order α, are obtained.

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Bu Makaleye Atıf Yap

KUMAR, V., CHO, N. E. (2022). Hermitian–Toeplitz determinants for functions with bounded turning. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 6, 2678–2687. https://ajindex.com/articles/607448

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Kaynakça (15)

  1. Ali RM. Coefficients of the inverse of strongly starlike functions. Bulletin of the Malaysian Mathematical Sciences Society 2003; 26 (1): 63-71
  2. Ali MF, Thomas DK, Vasudevarao A. Toeplitz determinants whose elements are the coefficients of analytic and univalent functions. Bulletin of the Australian Mathematical Society 2018; 97: 253-264
  3. Altınkaya Ş, Yalçın S. Upper bound of second Hankel determinant for bi-Bazilevič functions. Mediterranean Journal of Mathematics 2016; 13 (6): 4081-4090
  4. Arif M, Ullah I, Raza M, Zaprawa P. Investigation of the fifth Hankel determinant for a family of functions with bounded turnings. Mathematica Slovaca 2020; 70 (2): 319-328
  5. Bättcher A, Grudsky SM. Infinite Toeplitz matrices. In: Toeplitz matrices, asymptotic linear algebra and functional analysis. Texts and readings in mathematics (2000), Hindustan Book Agency, Gurgaon
  6. Bogoya JM, Böttcher A, Grudsky SM, Maximenko EA. Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols. Journal of Mathematical Analysis and Applications 2015; 422(2): 1308-1334
  7. Bouras B. Hankel determinants of a linear combination of three successive Catalan numbers. Mediterranean Journal of Mathematics 2013; 10 (2): 693-705
  8. Chan NN, Kwong MK. Hermitian matrix inequalities and a conjecture, The American Mathematical Monthly 1985; 92 (8): 533-541
  9. Cho NE, Kumar V, Kwon OS, Sim YJ. Coefficient bounds for certain subclasses of starlike functions. Journal of Inequalities and Applications 2019; Paper No. 276: 13 pp
  10. Cho NE, Kumar S., Kumar V. Coefficient functionals for starlike functions associated with the modified sigmoid function and the Bell numbers, Asian-European Journal of Mathematics 2021. doi:10.1142/S1793557122500425
  11. Cho NE, Kumar V, Kwon OS, Sim YJ. Sharp coefficient bounds for certain p−valent functions. Bulletin of the Malaysian Mathematical Sciences Society 2019; 42: 405-416
  12. Cudna K, Kwon OS, Lecko A, Sim YJ, Smiarowska B. The second and third-order Hermitian-Toeplitz determinants for starlike and convex functions of order α. Boletán de la Sociedad Matemática Mexicana 2020; 26 (2): 361-375
  13. Deniz E, Budak L. Second Hankel determinat for certain analytic functions satisfying subordinate condition. Mathematica Slovaca 2018; 68 (2): 463-471
  14. Goodman AW. Univalent functions, vol. I: Mariner, Tampa 1983
  15. Gray RM. Toeplitz and circulant matrices: A Review, Foundations and Trends in Communications and Informat