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Dergiler / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 3

The radii of starlikeness and convexity of the functions including derivatives of Bessel functions

Sercan KAZIMOĞLU
Erhan DENİZ
Sayfa
894–911
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The key tools in the proof of our main results are the Mittag–Leffler expansion for function $N_ν(z)$and properties of real and complex zeros of it.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let Jν(z) denote the Bessel function of the first kind of order ν.
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Temel Bulgular & Veri:In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_ν(z) = az^2 J ′′ _ν (z) + bzJ′_ν(z) + cJ_ν(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary.
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Sonuç & Katkı:The key tools in the proof of our main results are the Mittag–Leffler expansion for function $N_ν(z)$and properties of real and complex zeros of it.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Let Jν(z) denote the Bessel function of the first kind of order ν. In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_ν(z) = az^2 J ′′ _ν (z) + bzJ′_ν(z) + cJ_ν(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag–Leffler expansion for function $N_ν(z)$and properties of real and complex zeros of it.

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Bu Makaleye Atıf Yap

KAZIMOĞLU, S., DENİZ, E. (2022). The radii of starlikeness and convexity of the functions including derivatives of Bessel functions. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 3, 894–911. https://ajindex.com/articles/604168

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Kaynakça (18)

  1. Baricz Á, Kupán PA, Szász R. The radius of starlikeness of normalized Bessel functions of the first kind. Proceedings of American Mathematical Society 2014; 142 (5): 2019-2025
  2. Baricz Á, Szász R. The radius of convexity of normalized Bessel functions of the first kind. Analysis and Applications 2014; 12 (5): 485-509
  3. Baricz Á, Szász R. The radius of convexity of normalized Bessel functions. Analysis Mathematica 2015; 41 (3): 141-151
  4. Baricz Á, Çağlar M, Deniz E. Starlikeness of bessel functions and their derivatives. Mathematical Inequalities and Applications 2016; 19 (2): 439-449
  5. Baricz Á, Orhan H, Szász R. The radius of α−convexity of normalized Bessel functions of the first kind. Computational Methods and Function Theory 2016; 16 (1): 93-103
  6. Brown RK. Univalence of Bessel functions. Proceedings of the American Mathematical Society 1960; 11 (2): 278-283
  7. Çağlar M, Deniz E, Szász R. Radii of α−convexity of some normalized Bessel functions of the first kind. Results in Mathematics 2017; 72 (4): 2023-2035
  8. Deniz E, Szász R. The radius of uniform convexity of Bessel functions. Journal of Mathematical Analysis and Applications 2017; 453 (1): 572-588
  9. Deniz E, Kazımoğlu S, Çağlar M. Radii of Starlikeness and Convexity of Bessel Function Derivatives. Ukrains’kyi Matematychnyi Zhurnal 2021; 73 (11): 1461-1482
  10. Ismail MEH, Muldoon ME. Bounds for the small real and purely imaginary zeros of Bessel and related functions. Methods and Applications of Analysis 1995; 2 (1): 1-21
  11. Jensen JLWV. Recherches sur la théorie des équations. Acta Mathematica 1913; 36 (1): 181-195
  12. Kazımoğlu S, Deniz E. Geometric Properties of Function $az^2J′′_ν (z) + bzJ′_ν(z) + cJ_ν(z)$. arXiv:2006.13732v1 2020
  13. Kreyszig E, Todd J. The radius of univalence of Bessel functions. Illinois Journal of Mathematics 1960; 4 (1): 143–149
  14. Levin BY. Lectures on Entire Functions. American Mathematical Society Translations of Mathematical Monographs, 1996
  15. Mercer AMCD. The zeros of $az^2J′′_ν (z)+bzJ′_ν(z)+cJ_ν(z)$ as functions of order. International Journal of Mathematics and Mathematical Sciences 1992; 15: 319-322
  16. Olver FWJ, Lozier DW, Boisvert RF, Clark CW. (Eds.), NIST Handbook of Mathematical Functions. Cambridge Univ. Press, Cambridge, 2010
  17. Shah SM, Trimble SY. Entire functions with univalent derivatives. Journal of Mathematical Analysis and Applications 1971; 33: 220-229
  18. Szász R. About the radius of starlikeness