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- MakaleAçık Erişim2020Scopus SJRQ2Geometric and monotonic properties of hyper-Bessel functions
Aktaş, İbrahim; Baricz, Árpád; Singh, Sanjeev
Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some transcendental equations. In addition, we give some bounds for the first positive zero of normalized hyper-Bessel functions, Redheffer-type inequalities, and bounds for this function. In this study we take advantage of Euler–Rayleigh inequalities and Laguerre–Pólya class of real entire functions, intensively.
AtıfScopus21WoS26OpenAlex26İncele - MakaleAçık Erişim2018Scopus SJRQ2Bounds for radii of starlikeness and convexity of some special functions
Aktaş, Ibrahim; Baricz, Árpád; Orhan, Halit
In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler-Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-Pólya class of real entire functions plays an important role in our study.
AtıfScopus37WoS36TR Dizin7İncele