Radii of starlikeness and convexity of generalized Struve functions

Year 2020, Volume: 49 Issue: 4, 1216 - 1233, 06.08.2020

Evrim Toklu

https://doi.org/10.15672/hujms.518154

Cited By: 3

Abstract

In this paper, it is aimed to determine the radii of starlikeness and convexity of the normalized generalized Struve functions for three different kinds of normalization and to find tight lower and upper bounds for the radius of starlikeness and convexity of these normalized Struve functions by making use of Euler-Rayleigh inequalities. The Laguerre-Polya class of entire functions has a crucial role in constructing our main results. *********************************************************************

Keywords

generalized Struve functions, univalent, starlike and convex functions, radius of starlikeness and convexity, Mittag-Leffler expansions, Laguerre-Polya class of entire functions

References

• [1] İ. Aktaş and Á. Baricz, Bounds for radii of starlikeness of some q−Bessel functions, Results Math. 72, 947–963, 2017.
• [2] İ. Aktaş, Á. Baricz, and H. Orhan, Bounds for radii of starlikeness and convexity of some special functions, Turkish J. Math. 42, 211–226, 2018.
• [3] 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.
• [4] İ. Aktaş, E. Toklu, and H. Orhan, Radii of uniform convexity of some special functions, Turkish J. Math. 42, 3010–3024, 2018.
• [5] Á. Baricz, Generalized Bessel function of first kind, Lecture Notes in Mathematics, Springer, Berlin, 2010.
• [6] Á. Baricz, D.K. Dimitrov, H. Orhan, and N. Yağmur, Radii of starlikeness of some special functions, Proc. Amer. Math. Soc. 144, 3355–3367, 2016.
• [7] Á. Baricz, P.A. Kupán and R. Szász, The radius of starlikeness of normalized Bessel functions of the first kind, Proc. Amer. Math. Soc. 142 (6), 2019–2025, 2014.
• [8] Á. Baricz, H. Orhan, and R. Szász, The radius of α− convexity of normalized Bessel functions of the first kind, Comput. Methods Funct. Theory 16 (1), 93–103, 2016.
• [9] Á. Baricz and S. Sanjeev, Zeros of some special entire functions, Proc. Amer. Math. Soc. 146 (5), 2207–2216, 2018.
• [10] Á. Baricz and R. Szász, The radius of convexity of normalized Bessel functions, Anal. Math. 41 (3), 141–151, 2015.
• [11] Á. Baricz and R. Szász, The radius of convexity of normalized Bessel functions of the first kind, Anal. Appl. (Singap.) 12 (5), 485–509, 2014.
• [12] Á. Baricz, E. Toklu, and E. Kadıoğlu, Radii of starlikeness and convexity of Wright functions, Math. Commun. 23, 97–117, 2018.
• [13] N. Bohra and V. Ravichandran, Radii problems for normalized Bessel functions of the first kind, Comput. Methods Funct. Theory 18, 99–123, 2018.
• [14] R.K. Brown, Univalence of Bessel functions, Proc. Amer. Math. Soc. 11, 278–283, 1960.
• [15] E. Deniz and R. Szász, The radius of uniform convexity of Bessel functions, J. Math. Anal. 453 (1), 572–588, 2017.
• [16] D.K. Dimitrov and Y.B. Cheikh, Laguerre polynomials as Jensen polynomials of Laguerre-Pólya entire functions, J. Comput. Appl. Math. 233, 703–707, 2009.
• [17] P.L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer, New York, 1983.
• [18] E. Kreyszig and J. Todd, The radius of univalence of Bessel functions, Illinois J. Math. 4, 143–149, 1960.
• [19] H.-J. Runckel, Zeros of entire functions, Trans. Amer. Math. Soc. 143, 343–362, 1969.
• [20] G.N. Watson, A Treatise of the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1944.
• [21] H.S. Wilf, The radius of univalence of certain entire functions, Illinois J. Math. 6 (2), 242–244, 1962.