Related papers: Radii of starlikeness of some special functions
The radii of convexity of some Lommel and Struve functions of the first kind are determined. For both of Lommel and Struve functions three different normalizations are applied in such a way that the resulting functions are analytic in the…
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 combination of special functions we obtain tight lower and upper…
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…
Tight lower and upper bounds for the radius of univalence of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve…
For normalised analytic functions $f$ defined on the open unit disc $\mathbb{D}$ satisfying the condition $\sup_{z\in \mathbb{D}}(1-|z^2|) |f'(z)|\leq 1$, known as Bloch functions, we determine various starlikeness radii.
We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star…
In this paper our aim is to determine the radii of univalence, starlikeness and convexity of the normalized regular Coulomb wave functions for two different kinds of normalization. The key tools in the proof of our main results are the…
This paper studies analytic functions $f$ defined on the open unit disk of the complex plane for which $f/g$ and $(1+z)g/z$ are both functions with positive real part for some analytic function $g$. We determine radius constants of these…
Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of Bernoulli lemniscate starlikeness, and…
We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class…
Motivated by the pioneering work of M.S. Robertson [Ro54] and R.K. Brown [Br60], [Br62], who examined the geometric properties of some normalised solutions of second-order homogeneous differential equations, in this paper we investigate the…
A starlike univalent function $f$ is characterized by the function $zf'(z)/f(z)$; several subclasses of these functions were studied in the past by restricting the function $zf'(z)/f(z)$ to take values in a region $\Omega$ on the right-half…
We investigate harmonic mappings $f=h+\bar{g}$ defined in the unit disk, where $g$ and $h$ satisfy certain prescribed conditions and the analytic part $h$ belongs to the Ma and Minda class of starlike functions. Certain sharp radius results…
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…
We consider normalized analytic function $f$ on the open unit disk for which either $\operatorname{Re} f(z)/g(z)>0$, $|f(z) /g(z) - 1|<1$ or $\operatorname{Re} (1-z^2) f(z) /z>0$ for some analytic function $g$ with $\operatorname{Re}…
The radii of $\alpha$-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 $\alpha\in[0,1],$ and they are…
The radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1$, have been determined for normalizations of $q$-Bessel function, Bessel function of first kind…
In this paper we deal with the radii of starlikeness and convexity of the $q-$Mittag--Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are…
Sufficient conditions are obtained on the parameters of Lommel function of the first kind, generalized Struve function of the first kind and the confluent hypergeometric function under which these special functions become exponential convex…
In this manuscript, we deal with three classes of quotient functions having fixed second coefficient described on open unit disk. The radius of strongly starlikeness, lemniscate starlikeness, lune starlikeness, parabolic starlikeness, sine…