arXiv subjects

Md Nurezzaman

Publications and source records attributed to Md Nurezzaman.

4 recordsLinked to original sources

arXiv2025

On analytic functions related to Booth-lemniscate

For $0\le α\le 1 $, let $\mathcal{BS}(α)$ be the class of all analytic functions in the unit disk $\mathbb{D}:=\{~z\in\mathbb{C}:|z|<1\}$ with normalization $f(0)=0$ and $f'(0)=1$ that satisfy the subordinate relation $zf'(z)/f(z)-1\prec z/(1-αz^2)$ and $\mathcal{BK}(α)$ be the class of all functions $f$ for which $zf' \in \mathcal{BS}(α)$. In this article, we obtain a sharp estimate of the initial Taylor coefficients and logarithmic coefficients for functions in the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. Further, we obtain the radius of convexity and study the pre-Schwarzian norm for the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$.

math.CV↗

arXiv2025

On close-to-convex functions

We consider a new subclass $\widetilde{\mathcal{K}}_u$ of close-to-convex functions in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$. For this class, we obtain sharp estimates of the Fekete-Szegö problem, growth and distortion theorem, radius of convexity and estimate of the pre-Schwarzian norm.

math.CV↗

arXiv2025

On a certain class of starlike functions

Let $\mathcal{S}_u^*$ denote the class of all analytic functions $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfies the inequality $\left|zf'(z)/f(z)-1\right|<1$ in $\mathbb{D}$. In the present article, we obtain the sharp estimate of Hankel determinants whose entries are coefficients of $f\in\mathcal{S}_u^*$, logarithmic coefficients of $f\in\mathcal{S}_u^*$ and coefficients of inverse of $f\in\mathcal{S}_u^*$, respectively. We also obtain, the sharp estimate of the successive coefficients for functions in the class $\mathcal{S}_u^*$.

math.CV↗

arXiv2024

Pre-Schwarzian norm estimate for certain Ma-Minda Class of functions

Let $\mathcal{S}^*(φ)$ be the class of all analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfy the subordination relation $zf'(z)/f(z)\precφ(z)$, where $φ$ is an analytic and univalent in $\mathbb{D}$ with ${\rm Re\,}φ(z)>0$ such that $φ(\mathbb{D})$ is symmetric with respect to the real axis and stralike with respect to $1$. In the present article, we obtain the sharp estimates of the pre-Schwarzian norm of $f$ and the Alexander transformation $J[f]$ for functions $f(z)$ in the class $\mathcal{S}^*(φ)$ when $φ(z)=e^{λz}$, $0<λ\leπ/2$ and $φ(z)=\sqrt{1+cz}$, $0<c\le1.$

math.CV↗