Related papers: $\mathcal{S}^{*}(\phi)$ and $\mathcal{C}(\phi)$-ra…

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 2011, Sok\'{o}{\l} (Comput. Math. Appl. 62, 611--619) introduced and studied the class $\mathcal{SK}(\alpha)$ as a certain subclass of starlike functions, consists of all functions $f$ ($f(0)=0=f'(0)-1$) which satisfy in the following…

For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,}…

Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion…

Logarithmic and inverse logarithmic coefficients play a crucial role in the theory of univalent functions. In this study, we focus on the class of starlike functions \(\mathcal{S}^*_\rho\), defined as \[ \mathcal{S}^*_\rho = \left\{ f \in…

The object of the present paper is to introduce and investigate two new general subclasses ${{S}^{*}}C(\alpha ,\beta ;\gamma )$ and $T{{S}^{*}}C(\alpha ,\beta ;\gamma )~~(\alpha, \beta \in [0,1),~\gamma \in [0,1])$ of the analytic…

Let $S^{*}(1-b)$ ($b \not= 0$ complex) denote the class of functions $f(z)=z+\alpha_{2}z^{2}+...$ analytic in $D={z \mid | z | < 1}$ which satisfies,for $z=e^{i\theta} \in D$, $(f(z)/z)\not= 0$ in D, and $Re \Biggr [ 1+ {1 \over b} \Biggr…

For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma…

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. In the present article, we obtain the sharp estimates of the Schwarzian norm for…

Let $G$ be a finite group, let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, and let $\alpha \colon G \to \operatorname{Aut} (A)$ be a tracially strictly approximately inner action of $G$ on $A$. Then the radius of…

For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=0, P. T. Mocanu (Mathematica (Cluj), 11(34) (1969)) have considered Mocanu functions. The object of the present paper is to discuss some sufficient problems for f(z) to…

We introduce the class of analytic functions $$\mathcal{F}(\psi):= \left\{f\in \mathcal{A}: \left(\frac{zf'(z)}{f(z)}-1\right) \prec \psi(z),\; \psi(0)=0 \right\},$$ where $\psi$ is univalent and establish the growth theorem with some…

Let $\phi$ be a normalized convex function defined on open unit disk $\mathbb{D}$. For a unified class of normalized analytic functions which satisfy the second order differential subordination $f'(z)+ \alpha z f''(z) \prec \phi(z)$ for all…

In 1984, Clunie and Sheil-Small proved that a sense-preserving harmonic function whose analytic part is convex, is univalent and close-to-convex. In this paper, certain cases are discussed under which the conclusion of this result can be…

The authors consider the class $\F$ of normalized functions $f$ analytic in the unit disk $\ID$ and satisfying the condition $${\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2},\quad z\in\D. $$ Recently, Ponnusamy et al.…

Let ${\mathcal M}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition $$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right…

In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions…

Let $\mathcal{A}$ denote the class of analytic functions $f$ on the unit disk $\mathbb{D}=\{z\in\mathbb{C} : |z|<1\}$, normalized by $f(0)=0$ and $f^{\prime}(0)=1$. For $-\pi/2<\alpha<\pi/2$, let $\mathcal{S}_{\alpha}$ be the subclass of…

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…

The discrete orthogonality of special function families, called $C$- and $S$-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivn\'ak and Patera (2009 J. Phys. A: Math. Theor. 42 385208).…