arXiv subjects

Sercan Topkaya

Publications and source records attributed to Sercan Topkaya.

3 recordsLinked to original sources

arXiv2018

Geometric Properties of Bessel function derivatives

In this paper our aim is to find the radii of starlikeness and convexity of Bessel function derivatives for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for nth derivative of Bessel function and properties of real zeros of it. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized nth derivative of Bessel function. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind.

math.CV↗

arXiv2018

The General Subclasses of the Analytic Functions and Their Various Properties

The object of the present paper is to introduce and investigate two new general subclasses ${{S}^{*}}C(α,β;γ)$ and $T{{S}^{*}}C(α,β;γ)~~(α, β\in [0,1),~γ\in [0,1])$ of the analytic functions. Here, we give sufficient conditions as well as necessary and sufficient conditions for the functions belonging to the classes.

math.CV↗

arXiv2017

Radii of the $β-$uniformly convex of order $α$ of Lommel and Struve functions

In this paper, we determine the radii of $β-$uniformly convex of order $α$ for three kinds of normalized Lommel and Struve functions of the first kind. In the cases considered the normalized Lommel and Struve functions are $β-$uniformly convex functions of order $α$ on the determined disks. The basic tool of this study is Lommel and Struve functions in series.

math.CV↗