On some properties of generalized Struve function

Year 2020, Volume: 69 Issue: 1, 347 - 353, 30.06.2020

İbrahim Aktaş , Halit Orhan , Dorina Raducanu

https://doi.org/10.31801/cfsuasmas.595570

Abstract

The main purpose of this investigation is to present some monotonic and log-concavity properties of the generalized Struve function. By using Hadamard product representation of the generalized Struve function, we investigate the sign of this function on some sets. Also, we determine an interval such that the generalized Struve function is decreasing in this interval. Moreover, we show that generalized Struve function is strictly logaritmically concave on some intervals. In addition, we prove that a function related to generalized Struve function is increasing function on R.

Keywords

Gamma function, generalized Struve function, log-concavity, monotonicity

References

• Aktaş, İ. On some properties of hyper-Bessel and related functions, TWMS J. App. Eng. Math., 9(1) (2019), 30--37.
• Aktaş, İ. Baricz, Á. and Orhan, H., Bounds for the radii of starlikeness and convexity of some special functions, Turk. J. Math., 42(1) (2018), 211--226.
• Aktaş, İ., Baricz, Á. and Singh, S. Geometric and monotonic properties of hyper-Bessel functions, Ramanujan J., doi.org/10.1007/s11139-018-0105-9
• Baricz, Á. Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73 (2008), 155--178.
• Baricz, Á. and Pogány, T. K. Functional inequalities of modified Struve functions, P. Roy. Soc. Edinb. A, 144(5) (2014), 891--904.
• Biernacki, M. and Krzyż, J. On the monotonity of certain functionals in the theory of analytic functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 9 (1955), 135--147.
• Mohtasami Borzadaran, G. R. and Mohtasami Borzadaran, H. A. Log-Concavity property for some well-known distributions, Surv. Math. Appl., 6 (2011), 203--219.
• Mondal, S.R. and Akel, M.S. Differential equation and inequalities of the generalized k-Bessel functions, J. Inequal. Appl., 2018:175 (2018).
• Srivastava, H. M. and Bansal, D. Close-to-convexity of a certain family of q-Mittag-Leffler functions, J. Nonlinear Var. Anal., 1 (2017), 61--69.
• Srivastava H.M., Murugusundaramoorthy G. and Janani T. Uniformly Starlike Functions and Uniformly Convex Functions Associated with the Struve Function, J. Appl. Computat. Math., 3: 180. doi: 10.4172/2168-9679.1000180
• Srivastava, H. M., Murugusundaramoorthy, G. and Sivasubramanian, S. Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integr. Transforms Spec. Funct., 18 (2007), 511--520.
• Toklu, E. Radii of starlikeness and convexity of generalized Struve functions, Hacettepe J. Math. Stat., (Accepted).