Related papers: Starlike Functions Associated with a Non-Convex Do…
Recent advances in image and signal processing have drawn on geometric function theory, particularly coefficient estimate problems. Motivated by their significance, we introduce a class of starlike functions related to a balloon-shaped…
We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid…
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…
In this paper, we introduce and explore a new class of starlike functions denoted by $\mathcal{S}^*_{\mathfrak{B}}$, defined as follows: $$\mathcal{S}^*_{\mathfrak{B}}=\{f\in \mathcal{A}:zf'(z)/f(z)\prec…
In the present investigation, we consider a subclass of starlike functions associated with a petal shaped domain, recently introduced and defined by $$\mathcal{S}^{*}_{\rho}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\sinh^{-1} z\}.$$ We…
In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class…
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…
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 $…
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…
In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new class…
This paper deals with some radius results and inclusion relations that are established for functions in a newly defined subclass of starlike functions associated with a petal shaped domain.
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…
In the present investigation, we employ a new technique to find several first and second order differential subordination implications involving the following starlike class associated with a bean shaped domain: \begin{equation*}…
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).…
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…
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…
In this paper, we investigate two subclasses of analytic and univalent functions associated with the exponential mapping $\varphi(z)=e^{\alpha z},\qquad 0<\alpha\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec…
This paper presents several results concerning second and third-order differential subordination for the class $\mathcal{S}^{*}_{e}:=\{f\in \mathcal{A}:zf'(z)/f(z)\prec e^z\}$, which represents the class of starlike functions associated…
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…
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…