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Sujoy Majumder

Publications and source records attributed to Sujoy Majumder.

At least 19 recordsLinked to original sources
arXiv2026

Meromorphic functions together with their partial derivatives sharing zeros and poles in $\mathbb{C}^m$

In the paper, using Nevanlinna's value distribution theory of meromorphic functions in $\mathbb{C}^m$, we study the problem: Let $f$ and $g$ be two finite order non-constant meromorphic functions in $\mathbb{C}^m$ such that $f$ and $g$ share $0$ and $\infty$ CM. If $\partial_{z_i}(f)$ and $\partial_{z_i}(g)$ share $0$ CM and if for one $n>1$, $\partial^n_{z_i}(f)$ and $\partial^n_{z_i}(g)$ share $0$ CM, where $i=1,2,\ldots,m$, then $f$ and $g$ have special presentations. Our finding extends the result of Köhler (Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros, Complex Var., 11 (1989), 39-48) into higher dimensions. Moreover, we show by an example that the restriction on the growth of $f$ and $g$ is necessary.

math.CV↗
arXiv2026

Entire solutions of Fermat-Type Partial Differential-Difference equations in higher dimensions

The purpose of this paper is to investigate the finite-order entire solutions of the following Fermat-type partial differential-difference equations: \begin{align*} (P_1(z)f(z+c))^{m_1}+\left(P_2(z)f(z)+\sideset{}{_{j=1}^m}{\sum} Q_j(z)\partial_{z_j}(f(z))\right)^{m_2}=P(z), \end{align*} \begin{align*} (P_1(z)f(z))^{m_1}+\left(P_2(z)f(z+c)+\sideset{}{_{j=1}^m}{\sum} Q_j(z)\partial_{z_j}(f(z))\right)^{m_2}=P(z) \end{align*} and \begin{align*} \left(\sideset{}{_{j=1}^m}{\sum} Q_j(z)\partial_{z_j}(f(z))\right)^{m_1}+\left(P_1(z)f(z+c)+P_2(z)f(z)\right)^{m_2}=P(z), \end{align*} in $\mathbb{C}^m$, where $m_1,m_2\in\mathbb{N}$ such that $m_1+m_2>2$, $c=(c_1,c_2,\ldots,c_m)\in\mathbb{C}^m$, $P(\not\equiv 0)$, $P_1$, $P_2$ and $Q_i\;(i=1,2,\ldots,m)$ are polynomials in $\mathbb{C}^m$ such that $P(z)$ is irreducible in $\mathbb{C}^m$. The results established in this paper generalize those of Xu et al. \cite{Xu-Luo-Cao-2025} from $\mathbb{C}$ to $\mathbb{C}^m$.

math.CV↗
arXiv2026

On coefficient theorems for starlike and quasi-convex of type B mappings in complex Banach spaces

In this paper, we study biholomorphic mappings $F: \mathbb{B} \to X$ of the form $F(z) = f(z)z$ for $z \in \mathbb{B}$, where $f: \mathbb{B} \to \mathbb{C}$ is a holomorphic function satisfying $f(0) = 1$ and $X$ is a complex Banach space with the unit ball $\mathbb{B}$. The main contributions of this paper are threefold. First, we establish a sufficient coefficient condition for a function $F(z)=zf(z)$ to be starlike and quasi-convex of type $B$ in a complex Banach space. Second, we prove that the Bieberbach conjecture holds for these classes of functions. Finally, we analyze the difference of coefficients for such functions in this setting. The results established here directly extend the previous results to the broader setting of complex Banach spaces.

math.CV↗
arXiv2026

Alpha-convex functions in complex Banach spaces

Let $\mathbb{B}$ be the unit ball in a complex Banach space ${\mathbb X}$. We study biholomorphic mappings $F: \mathbb{B} \to {\mathbb X}$ of the form $F(z) = f(z)z$ for $z \in \mathbb{B}$, where $f: \mathbb{B} \to \mathbb{C}$ is a holomorphic function satisfying $f(0) = 1$. Our main contributions are as follows: Inclusion Results: We establish inclusion conditions for $\mathcal{M}_α(\mathbb{B})$, class of $α$-convex functions in $\mathbb{B}$ to belong to the classes of starlike mappings or quasi-convex mappings of type $B$ on $\mathbb{B}$ for specified ranges of $α$. Characterization: We prove that $F(z) = \frac{f(l_{u}(z))}{l_{u}(z)}z \in \mathcal{M}_α(\mathbb{B})$ if and only if $f \in \mathcal{M}_α(\mathbb{U})$, where $f \in \mathcal{S}(\mathbb{U})$, $u \in {\mathbb X}$ with $\|u\| = 1$, and $l_{u} \in T(u)$. Duality: We present a duality relationship between the classes $\mathcal{S}^*(\mathbb{U})$ and $\mathcal{M}_α(\mathbb{B})$ for $α\ge 0$. Hankel Determinant Bounds: We determine sharp upper bounds for the second Hankel determinant of mappings in $\mathcal{M}_α(\mathbb{B})$ when $α\ge 0$. The results established here directly extend the previous results to the broader setting of complex Banach spaces.

math.CV↗
arXiv2026

Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order $α$ and Quasi-Convex Mappings of Type $B$ in Complex Banach Spaces

In this paper, we introduce and investigate a parameterized Hankel-type functional $$H_{2,2}^μ(f)=μa_2a_4-a_3^2,\qquad μ\in[0,1], $$ which reduces to the classical second-order Hankel determinant $H_{2,2}(f)$ when $μ=1$. We obtain estimates for $H_{2,2}^μ(f)$ over the class of starlike mappings of order $α$ on the unit ball of a complex Banach space and on the unit polydisk $\mathbb{U}^n$ in $\mathbb{C}^n$. We also establish estimates for $H_{2,2}^μ(f)$ over the class of quasi-convex mappings of type $B$ on the unit ball of a complex Banach space and on the unit polydisk $\mathbb{U}^n$. For $μ=1$, our results recover the corresponding estimates for the classical Hankel determinant and extend the known one-dimensional results of Cho et al. \cite{Cho-2018} and Thomas et al. \cite{Thomas-Tuneski} to higher-dimensional settings.

math.CV↗
arXiv2026

The Fekete-Szegö problem for starlike mappings of order $α$ and quasi-convex mappings of type $B$ in the unit balls of complex Banach spaces

We establish sharp estimates for the generalized Zalcman functional corresponding to the index $n=2$ for normalized starlike mappings of order $α$ and normalized quasi-convex mappings of type $B$ in the unit ball of a complex Banach space and on the unit polydisk in $\mathbb{C}^n$. We also derive sharp Fekete-Szegö inequalities for normalized starlike mappings of order $α$ and normalized quasi-convex mappings of type $B$ in the unit ball of a complex Banach space. Our results extend classical coefficient estimates to higher-dimensional holomorphic mappings and provide a partial confirmation of the generalized Zalcman conjecture in higher dimensions.

math.CV↗
arXiv2026

Toeplitz determinants for starlike mappings of order α in several complex variables

Let $F(z)=zf(z)$, where $f$ is a normalized scalar holomorphic function on the unit ball $\mathbb B$ of a complex Banach space $X$ or on the unit polydisk $\mathbb U^n$ of $\mathbb{C}^n$. We establish sharp bounds for two Toeplitz determinants involving the second, third and fourth Fréchet derivatives of $F$ when $F$ is starlike of order $α$, $0\leqα<1$. The first bound is sharp for the full range $0\leqα<1$, while the second is sharp for $0\leqα\leq 2/3$. The extremal mappings are explicitly identified, confirming the sharpness of the estimates.

math.CV↗
arXiv2026

Sharp Robertson-type coefficient estimates for radial starlike and quasi-convex of type B mappings of order α in complex Banach spaces

In this paper, we study biholomorphic mappings $F: \mathbb{B} \to X$ of the form $F(z) = f(z)z$ for $z \in \mathbb{B}$, where $f: \mathbb{B} \to \mathbb{C}$ is a holomorphic function satisfying $f(0) = 1$. Our main contributions are as follows: We establish sharp estimates for the coefficients of starlike functions of order $α$ as well as quasi-convex functions of type $B$ and order $α$ by employing the notion of majorization. The results established here directly extend the results due to Robertson \cite{Robertson-1936} to the broader setting of complex Banach spaces.

math.CV↗
arXiv2026

Logarithmic coefficients for exponential classes of starlike and convex functions

In this paper, we investigate two subclasses of univalent functions associated with the exponential mapping $φ(z)=e^{αz}, \ 0<α\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec e^{αz}\quad \text{and} \quad 1+\frac{zf''(z)}{f'(z)}\prec e^{αz}.$ These classes provide a natural exponential analogue of several classical subclasses arising in geometric function theory. We obtain sharp coefficient estimates, logarithmic coefficient inequalities and sharp bounds for the associated Hankel determinants. In particular, explicit estimates are derived for $H_{2,1}(F_f/2)$ for functions belonging to the exponential subclasses introduced above of starlike and convex functions. Our results extend and unify several earlier works on exponential subclasses and highlight connections with logarithmic coefficients and determinant functionals.

math.CV↗
arXiv2026

Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc

In this paper, we investigate Bohr-type inequalities for certain integral transforms of some bounded holomorphic operator-valued functions defined on a shifted disc. More precisely, we consider functions $f\in H^{\infty}(Ω_γ,\mathcal{B}(\mathcal{H}))$, where $\mathcal{B}(\mathcal{H})$ denotes the space of bounded linear operators on a complex Hilbert space $\mathcal{H}$, and study the Bohr phenomena associated with the series representations in \eqref{e1.2a} and \eqref{e2.1}. Moreover, we determine the sharp radii $R_γ>0$ for which the corresponding majorant series satisfy the required inequalities for all $|z|\leq R_γ$. One of our main results extends some recent result due to Kumar and Sahoo \cite{Kumar-Sahoo-Meditarr-2023} to a large extent, and the other one is new in the literature

math.CV↗
arXiv2026

Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in $\mathbb{C}^n$

The primary objective of this paper is to determine the existence and explicit form of finite-order entire solutions in $\mathbb{C}^n$ of the following system of Fermat-type partial differential-difference equations: \[\begin{cases} \left(\frac{\partial f_1\left(z\right)}{\partial z_1}\right)^{n_1} + (f_2 \left(z+c\right)-f_1(z) )^{m_1}= 1, \medskip \left(\frac{\partial f_2\left(z\right)}{\partial z_1}\right)^{n_2} + (f_1 \left(z+c \right)-f_2(z) )^{m_2}= 1, \end{cases}\] for several choices of the positive integers $n_1$, $n_2$, $m_1$, and $m_2$, where $c=(c_1,c_2,\ldots,c_n)$. We obtain structural classifications and nonexistence results in the exponent regimes specified in the main theorems, extending results of Xu et al. \cite{XLL1} from $\mathbb{C}^2$ to $\mathbb{C}^n$. Several examples illustrate the resulting solution families.

math.CV↗
arXiv2026

Coefficient Problems for a Ma-Minda Convex Class Associated with the Normalized Arcsine Mapping

Let $\mathcal{C}_{\arcsin}$ denote the Ma--Minda subclass of convex functions generated by the normalized arcsine mapping $φ(z)=1+\frac{2}π\arcsin z.$ For this family, we develop a unified coefficient analysis based on subordination techniques, Carathéodory functions and sharp estimates for Schwarz functions. As consequences, we derive sharp estimates for the initial Taylor coefficients, logarithmic coefficients and certain differences involving the logarithmic and inverse logarithmic coefficients. We further determine the exact bounds for the second Hankel determinant $H_{2,2}(f)$ together with the Hankel determinants $H_{2,1}(F_f/2)$ and $H_{2,1}(F_{f^{-1}}/2)$ associated with the logarithmic coefficients of a function and its inverse. Moreover, sharp estimates are obtained for the initial generalized Zalcman functional and the generalized Fekete--Szegö functional. In every case, the corresponding extremal functions are identified, showing that all of the obtained inequalities are best possible.

math.CV↗
arXiv2026

Coefficient estimates and Bohr phenomenon for pluriharmonic mappings in the polydisc

We introduce the class $\mathscr{P}_{\mathcal{H}_n^0}(α)$ $(0\leq α<1)$ of normalized pluriharmonic mappings in the setting of several complex variables. This class extends the harmonic family $\mathscr{P}_{\mathcal{H}}^{0}(α)$ to the multidimensional framework. We establish sharp coefficient estimates and growth theorems for functions in $\mathscr{P}_{\mathcal{H}_n^0}(α)$, thereby generalizing the corresponding results of Li and Ponnusamy \cite{Li-Ponnusamy-2013a} and Allu and Halder \cite{Allu-Halder-2021}. We further determine the associated Bohr radius and investigate the sections (partial sums) of functions in this class, obtaining quantitative results that describe the behavior of their truncated expansions.

math.CV↗
arXiv2026

Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function

In this paper, we study a Ma--Minda type subclass of starlike functions associated with the normalized arcsine function $φ(z)=1+\frac{2}π\arcsin z.$ Using the Carathéodory function approach together with sharp coefficient estimates for Schwarz functions, we obtain explicit sharp bounds for the initial Taylor coefficients and logarithmic coefficients of functions in this class. We also derive a sharp estimate for the second Hankel determinant \(H_{2,2}(f)\), as well as for the Hankel determinants \(H_{2,1}(F_f/2)\) and \(H_{2,1}(F_{f^{-1}}/2)\) associated with the logarithmic coefficients of a function and its inverse. In addition, we establish a sharp bound for a difference involving logarithmic coefficients. The extremal functions for all the main results are identified, confirming the sharpness of the estimates.

math.CV↗
arXiv2026

Coefficient bounds and growth estimates for a class of pluriharmonic mappings in unit polydisk

In this paper, we first introduce and study the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$ of normalized pluriharmonic mappings, characterized by a specific bound on the sum of their second-order partial derivatives. We prove a one-to-one correspondence between this pluriharmonic class and a class of holomorphic functions, extending the known result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2020} to the setting of several complex variables. Finally, we provide sharp coefficient bounds and growth estimates for functions in the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$.

math.CV↗
arXiv2026

Multidimensional analogues of the improved Bohr's inequality for shifted polydisks

In this article, we investigate the Bhor phenomenon for holomorphic functions defined on a general simply connected domain in $\mathbb{C}^n$. We improve the existing results Evdordis et al. (Improved Bohr's inequality for shifted disks, Results in Mathematics, 76, 14 (2021)) for a broader class of holomorphic functions in $\mathbb{C}^n$. Furthermore, we consider pluriharmonic mappings defined on a polydisk containing the unit polydisk $\mathbb{P}Δ(0_n, 1_n)$ and establish a Bohr-type inequality for this class of mappings.

math.CV↗
arXiv2026

On a class of pluriharmonic mappings in the unit polydisk

In this paper, we introduce and study the class $\mathcal{W}_{\mathcal{H}_n^0}(α)$ of normalized pluriharmonic mappings, characterized by a suitable bound on their second-order partial derivatives. We establish a one-to-one correspondence between this pluriharmonic class and an associated class of holomorphic functions, thereby extending a result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2019} to the setting of several complex variables. Furthermore, we obtain sharp coefficient bounds, growth estimates and a convex combination theorem for functions in $\mathcal{W}_{\mathcal{H}_n^0}(α)$. Finally, we introduce sections (partial sums) of pluriharmonic mappings and investigate their properties for functions belonging to $\mathcal{W}_{\mathcal{H}_n^0}(α)$.

math.CV↗