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In this paper, we provide an estimation for the sharp bound of the third Hankel determinant of starlike functions of order $\alpha$, where $\alpha$ ranges in the interval $[0, 1/6]\cup \{1/2\}$ and thereby extending the result of Rath et…

Complex Variables · Mathematics 2023-09-07 Neha Verma , S. Sivaprasad Kumar

For $\alpha\ge 0$, let $\mathcal{W}(\alpha)$ be the class of all analytic functions in the unit disk $\mathbb{D}$ with normalization $f(0) = 0 $ and $ f'(0) = 1 $ that satisfy the relation $Re\,\{f'(z) + \alpha z f''(z)\} > 0$. This article…

Complex Variables · Mathematics 2026-05-20 Chayani Dhara , Nirupam Ghosh

By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations.…

Complex Variables · Mathematics 2025-08-12 Ming Li , Ao-Li Zhu

Let $\mathcal{A}$ denote the class of analytic functions such that $f(0)=0$ and $f'(0)=1$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}.$ In this paper, we consider $\mathcal{S}^*(\varphi) := \left\{ f \in \mathcal{A} :…

Complex Variables · Mathematics 2026-04-14 Vasudevarao Allu , Shobhit Kumar

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…

Complex Variables · Mathematics 2023-03-28 Surya Giri , S. Sivaprasad Kumar

We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes…

Complex Variables · Mathematics 2022-07-07 Shalini Rana , Om Ahuja , Naveen Kumar Jain

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…

Complex Variables · Mathematics 2024-12-24 S. Sivaprasad Kumar , Arya Tripathi , Snehal Pannu

In the present investigation, we study the class of Sigmoid starlike functions, given by $\mathcal{S}^*_{SG}=\{f\in\mathcal{A}: {zf'(z)}/{f(z)}\prec 2/(1+e^{-z})\}$ in context of estimating the sharp radius constants associated with several…

Complex Variables · Mathematics 2022-08-03 Priyanka Goel , S. Sivaprasad Kumar

This paper aims to pursue some classes of normalized analytic functions $f$ with fixed second coefficient defined on open unit disk, such that ${(1+z)^2f(z)}/{z}$ and ${(1+z)f(z)}/{z}$ are functions having positive real part. The radius of…

Complex Variables · Mathematics 2022-03-17 Sushil Kumar , Swati Anand , Naveen Kumar Jain

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}…

Complex Variables · Mathematics 2024-12-09 S. Sivaprasad Kumar , Surya Giri

This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…

Complex Variables · Mathematics 2022-10-25 Surya Giri , S. Sivaprasad Kumar

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…

Complex Variables · Mathematics 2026-05-29 Shantanu Panja , Sujoy Majumder , Abhijit Banerjee

The aim of the present paper is to obtain the sharp bounds of the Hankel determinants H_2(3) and H_3(1) for the well known class SL^* of starlike functions associated with the right lemniscate of Bernoulli. Further for n=3, we find the…

Complex Variables · Mathematics 2022-08-23 Shagun Banga , S. Sivaprasad Kumar

Let $f$ be analutic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bound of Hankel determinant of the second order for the class of analytic unctions satisfying \[ \left|\arg…

Complex Variables · Mathematics 2019-03-20 Milutin Obradovic , Nikola Tuneski

Let $f$ be analytic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order $\alpha$,…

Complex Variables · Mathematics 2019-12-30 Milutin Obradovic , Nikola Tuneski

The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…

Complex Variables · Mathematics 2016-08-25 Md. Firoz Ali , A. Vasudevarao

For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{z {f}'(z)}{f(z) - f(-z)} \prec \varphi(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec \varphi(z),$$ denoted by…

Complex Variables · Mathematics 2022-10-25 Surya Giri , S. Sivaprasad Kumar

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…

Complex Variables · Mathematics 2020-01-22 Asha Sebastian , V. Ravichandran

In this paper, sharp bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.

Complex Variables · Mathematics 2022-08-16 Mridula Mundalia , S. Sivaprasad Kumar

In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic properties of these classes such as, subordination relations,…

Complex Variables · Mathematics 2018-11-26 Rahim Kargar