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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 1

On monotonic and logarithmic concavity properties of generalized $k$-Bessel function

İbrahim Aktaş(KARAMANOGLU MEHMETBEY UNIVERSITY)0000-0003-4570-4485
Pages
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Publication Date
2021-02-04
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In addition, by using the relationships between Bessel-type special functions and some basic functions, we present some specific examples related to the monotonic and log-concavity properties of some trigonometric and hyperbolic functions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, our main objective is to determine some monotonic and log-concavity properties of generalized $k$-Bessel function by using its Hadamard product representation and some earlier results on power series.
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Key Findings & Data:In this study, our main objective is to determine some monotonic and log-concavity properties of generalized $k$-Bessel function by using its Hadamard product representation and some earlier results on power series.
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Conclusion & Impact:In addition, by using the relationships between Bessel-type special functions and some basic functions, we present some specific examples related to the monotonic and log-concavity properties of some trigonometric and hyperbolic functions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$k$-Gamma functions · $k$-Bessel function · monotonicity

Abstract

In this study, our main objective is to determine some monotonic and log-concavity properties of generalized $k$-Bessel function by using its Hadamard product representation and some earlier results on power series. In addition, by using the relationships between Bessel-type special functions and some basic functions, we present some specific examples related to the monotonic and log-concavity properties of some trigonometric and hyperbolic functions.

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Cite This Article

Aktaş, İ. (2021). On monotonic and logarithmic concavity properties of generalized $k$-Bessel function. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.621072

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References (15)

  1. İ. Aktaş, On some properties of hyper-Bessel and related functions, TWMS J. App. and Eng. Math. 9 (1), 30–37, 2019.
  2. İ. Aktaş, Partial sums of Hyper-Bessel function with applications, Hacet. J. Math. Stat. 49 (1), 380–388, 2020.
  3. İ. Aktaş and Á. Baricz, Bounds for the radii of starlikeness of some q-Bessel functions, Results Math. 72 (1–2), 947–963, 2017.
  4. İ. Aktaş and H. Orhan, Bounds for the radii of convexity of some q-Bessel functions, Bull. Korean Math. Soc. 57 (2), 355–369, 2020.
  5. İ. Aktaş, Á. Baricz and H. Orhan, Bounds for the radii of starlikeness and convexity of some special functions, Turkish J. Math. 42 (1), 211–226, 2018.
  6. İ. Aktaş, Á. Baricz and S. Singh, Geometric and monotonic properties of hyper-Bessel functions, Ramanujan J. 51 (2), 275–295, 2020.
  7. İ. Aktaş, Á. Baricz and N. Yağmur, Bounds for the radii of univalence of some special functions, Math. Inequal. Appl. 20 (3), 825–843, 2017.
  8. Á. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen 73 (1–2), 155–178, 2008.
  9. Á. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Mathe- matics, Springer-Verlag, 2010.
  10. Á. Baricz and T.K. Pogány, Functional inequalities of modified Struve functions, Proc. Roy. Soc. Edinburgh Sect. A, 144 (5), 891–904, 2014.
  11. M. Biernacki and J. Krzyż, On the monotonity of certain functionals in the theory of analytic functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 9, 135–147, 1955.
  12. R. Díaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Mathemáticas, 15 (2), 179–192, 2007.
  13. G.R. Mohtasami Borzadaran and H.A. Mohtasami Borzadaran, Log-concavity prop- erty for some well-known distributions, Surv. Math. Appl. 6, 203–219, 2011.
  14. S.R. Mondal and M.S. Akel, Differential equation and inequalities of the generalized k-Bessel functions, J. Inequal. Appl., 2018:175. doi: 10.1186/s13660-018-1772-1
  15. E. Toklu, Radii of starlikeness and convexity of generalized k-Bessel functions, arXiv:1902.09979, 2019.