Róbert Szász

The radius of convexity of normalized Bessel functions of the first kind

The radii of

The radius of starlikeness of normalized Bessel functions of the first kind

\alpha

Close-to-Convexity of Some Special Functions and Their Derivatives

-convexity are deduced for three different kind of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when

On an identity for zeros of Bessel functions

\alpha\in[0,1],

Monotonicity properties of some Dini functions

and they are decreasing with respect to the parameter

The radius of uniform convexity of Bessel functions

\alpha.

The Radius of \(\alpha \)-Convexity of Normalized Bessel Functions of the First Kind

The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.

The radius of convexity of normalized Bessel functions

In this note our aim is to determine the radius of starlikeness of the normalized Bessel functions of the first kind for three different kinds of normalization. The key tool in the proof of our main result is the Mittag-Leffler expansion for Bessel functions of the first kind and the fact that, according to Ismail and Muldoon [IM2], the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind.

About the starlikeness of Bessel functions

In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of the first kind, which can be expressed in terms of the hypergeometric function