Related papers: Radius of starlikeness for some classes containing…

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a…

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…

In the present investigation, we introduce a new subclass of starlike functions defined by $\mathcal{S}^{*}_{\tau}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\arctan z=:\tau(z)\}$, where $\tau(z)$ maps the unit disk $\mathbb {D}:= \{z\in…

A starlike function $f$ is characterized by the quantity $zf'(z)/f(z)$ lying in the right half-plane. This paper deals with sharp bounds for certain symmetric Toeplitz determinants whose entries are the coefficients of the functions $f$ for…

Let $\mathcal{S}^*_{Ne}$ be the collection of all analytic functions $f(z)$ defined on the open unit disk $\mathbb{D}$ and satisfying the normalizations $f(0)=f'(0)-1=0$ such that the quantity $zf'(z)/f(z)$ assumes values from the range of…

By considering the polynomial function $\phi_{car}(z)=1+z+z^2/2,$ we define the class $\Scar$ consisting of normalized analytic functions $f$ such that $zf'/f$ is subordinate to $\phi_{car}$ in the unit disk. The inclusion relations and…

Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In…

Let $\mathcal{A}$ denote the class of all analytic functions $f$ defined in the open unit disc $\mathbb{D}$ with the normalization $f(0)=0=f'(0)-1$ and let $P'$ be the class of functions $f\in\mathcal{A}$ such that ${\rm{Re}}\,f'(z)>0$,…

We introduce and study a class of starlike functions associated with the non-convex domain \[ \mathcal{S}^*_{nc} = \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1+z}{\cos{z}} =: \varphi_{nc}(z), \;\; z \in \mathbb{D}…

For the family of analytic functions $f(z)$ in the open unit disk $\mathbb{D}$ with $f(0)=f'(0)-1=0$, satisfying the differential equation \begin{equation*} zf'(z) - f(z) = \dfrac{1}{2} z^2 \phi(z), \quad |\phi(z)| \leq 1, \end{equation*}…

Ma-Minda class (of starlike functions) consists of all normalized analytic functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is contained in the some starlike region in the right-half plane. We obtain the best possible…

For a function $f$ starlike of order $\alpha$, $0\leqslant \alpha <1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $\mathbb{D}$ and $\beta>0$, we consider the function $F:\mathbb{D}\to\mathbb{C}$…

Let ${\mathcal S}$ be the class of all functions $f$ that are analytic and univalent in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$. Let $\mathcal{U} (\lambda)$ denote the set of all $f\in {\mathcal S}$ satisfying the…

For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $…

We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1).…

In this study, we deal with the sharp bounds of certain Toeplitz determinants whose entries are the logarithmic coefficients of analytic univalent functions $f$ such that the quantity $z f'(z)/f(z)$ takes values in a specific domain lying…

For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator…

Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradovi\'{c} and Ponnusamy have…

In this paper, we introduce and explore a new class of starlike functions denoted by $\mathcal{S}^*_{\mathfrak{B}}$, defined as follows: $$\mathcal{S}^*_{\mathfrak{B}}=\{f\in \mathcal{A}:zf'(z)/f(z)\prec…

For a normalised analytic function f defined on the open unit disk in the complex plane, we determine several sufficient conditions for starlikeness in terms of the quotients Q_{ST}:=zf'(z)/f(z), Q_{CV}:=1+zf"(z)/f'(z) and the Schwarzian…