Partha Pratim Roy

activity

20232026

collaborators

13 papers

math.CV2026

The Bohr Phenomenon for Close-to-Convex Harmonic Mappings

Molla Basir Ahamed, Partha Pratim Roy

The classical Bohr inequality states that if $f (z) = \sum_{n = 0}^{\infty} a_{n} z^{n}$ is analytic and $∣ f (z) ∣ < 1$ in the unit disk $D$ , then $\sum_{n = 0}^{\infty} ∣ a_{n} ∣ r^{n} \leq 1$ …

math.CV2026

Moduli difference of initial inverse logarithmic coefficients for starlike and convex functions

Molla Basir Aahmed, Partha Pratim Roy

Let $A$ denote the class of functions $f$ that are analytic in the open unit disk $D$ and satisfy the normalization conditions $f (0) = 0$ and $f^{'} (0) = 1$ . This p…

math.CV2025

Bohr-Rogosinski Inequalities for bounded analytic functions

Molla Basir Aahmed, Partha Pratim Roy

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $B$ , which consists of analytic self-mappings defined on…

math.CV2025

Quasiconformal Extension of Meromorphic Functions with High-Order Poles

Molla Basir Ahamed, Partha Pratim Roy

In this paper, we study the class $Σ^{(m)} (p)$ of meromorphic univalent functions $f$ in $D$ with a pole of order $m \geq 1$ at $p \in (0, 1)$ , admitting a $k$ -quasicon…

math.CV2025

A Unified Study of Bohr's Inequality for analytic and harmonic mappings on the Unit Disk

Molla Basir Ahamed, Partha Pratim Roy, Sujoy Majumder

We investigate improved forms of the Bohr inequality, using the quantity $S_{r} / π$ , for analytic selfmaps in class $B$ of $D$ , where $S_{r}$ is the area measure of $…

math.CV2024

Sharp Bohr radius involving Schwarz functions for certain classes of analytic functions

Molla Basir Ahamed, Partha Pratim Roy

The Bohr radius for an arbitrary class $F$ of analytic functions of the form $f (z) = \sum_{n = 0}^{\infty} a_{n} z^{n}$ on the unit disk $D = {z \in C : ∣ z ∣ < 1}$ is…

math.CV2024

Bohr radius for invariant families of bounded analytic functions and certain Integral transforms

Molla Basir Ahamed, Partha Pratim Roy, Sabir Ahammed

In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $D$ . Then, we obtain Bohr inequality for certain i…

math.CV2024

The Bohr inequality on a simply connected domain and its applications

Sabir Ahammed, Molla Basir Ahamed, Partha Pratim Roy

In this article, we first establish a generalized Bohr inequality and examine its sharpness for a class of analytic functions $f$ in a simply connected domain $Ω_{γ},$ where $0\leq γ…

math.CV2024

Revisiting Bohr Inequalities with Analytic and Harmonic Mappings on unit disk

Molla Basir Ahamed, Partha Pratim Roy

In this paper, we study some improved and refined versions of the classical Bohr inequality applicable to the class $B$ , which consists of self-analytic mappings defined…

math.CV2024

Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings

Molla Basir Ahamed, Partha Pratim Roy

Let $H (Ω)$ be the class of complex-valued functions harmonic in $Ω \subset C$ and each $f = h + g \in H (Ω)$ , where $h$ and $g$ are analytic…

math.CV2023

Hankel and Toeplitz determinants of logarithmic coefficients of Inverse functions for certain classes of univalent functions

Sanju Mandal, Partha Pratim Roy, Molla Basir Ahamed

The Hankel and Toeplitz determinants $H_{2, 1} (F_{f^{- 1}} /2)$ and $T_{2, 1} (F_{f^{- 1}} /2)$ are defined as: \begin{align*} H_{2,1}(F_{f^{-1}}/2):= \begin{vmatrix} Γ_1 & Γ_2 Γ_2 & Γ_3…

math.CV2023

The third Hankel determinant for inverse coefficients of starlike functions of order 1/2

Molla Basir Ahamed, Partha Pratim Roy

The sharp bound for the third Hankel determinant for the coefficients of the inverse function of starlike function of order $1/2$ is obtained. In light of this, we can deduce that…

math.CV2023

Sharp bounds for second Hankel determinant of logarithmic coefficients for certain classes of univalent functions

Sanju Mandal, Partha Pratim Roy, Molla Basir Ahamed

The Hankel determinant $H_{2, 2} (F_{f} /2)$ is defined as: \begin{align*} H_{2,2}(F_{f}/2):= \begin{vmatrix} γ_2 & γ_3 γ_3 & γ_4 \end{vmatrix}, \end{align*} where $γ_{2}, γ_{3},$ and $γ_…