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

Year 2021, Volume: 50 Issue: 1, 180 - 187, 04.02.2021

İbrahim Aktaş

https://doi.org/10.15672/hujms.621072

Cited By: 5

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.

Keywords

$k$-Gamma functions , $k$-Bessel function , monotonicity , log-concavity

References

• [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.