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Nirupam Ghosh

Publications and source records attributed to Nirupam Ghosh.

7 recordsLinked to original sources
arXiv2026

Logarithmic Inverse Coefficients and Moduli Differences of Janowski Class

In this paper, we study the sharp bounds of the first three logarithmic inverse coefficients for Janowski convex class $\mathcal{C}(A, B)$. We also derive sharp upper and lower bounds of $\bigl|\,\gamma_2 \,\bigr|-\bigl|\,\gamma_1\,\bigr|$ and $\bigl|\,\Gamma_2 \,\bigr|-\bigl|\,\Gamma_1\,\bigr|$ for functions in the class $\mathcal{C}(A, B)$. Furthermore, a sharp estimate for the second Hankel determinant associated with the logarithmic inverse coefficients for functions in $\mathcal{C}(A, B)$ is obtained.

math.CV↗
arXiv2026

Logarithmic Coefficients Problems of Geometric Subclass of Closed-to-convex Functions

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 aims to establish sharp bounds for logarithmic coefficients $\gamma_1$, $\gamma_2$ and $\gamma_3$ and logarithmic inverse coefficients $\Gamma_1$, $\Gamma_2$ and $\Gamma_3$ of functions in $\mathcal{W}(\alpha)$. The sharp upper and lower bounds for $\bigl|\,\gamma_2 \,\bigr|-\bigl|\,\gamma_1\,\bigr|$ and $\bigl|\,\Gamma_2 \,\bigr|-\bigl|\,\Gamma_1\,\bigr|$ have been obtained for the class $\mathcal{W}{(\alpha)}$. In addition, we establish sharp inequality for the second Hankel determinant of the logarithmic and inverse logarithmic coefficients for the class $\mathcal{W}{(1)}$.

math.CV↗
arXiv2026

On posinormality of weighted composition-differentiation operators on $H^2(\mathbb{D})$

In this article, the posinormality and coposinormality of weighted composition-differentiation operators on Hardy space $H^2(\mathbb{D})$ are investigated. It is observed that while a composition-differentiation operator $D_{\phi,n}$ fails to be posinormal, the weighted composition-differentiation operator $D_{\psi,\phi,n}$ can be posinormal for specific choices of $\psi, \phi$. Some necessary conditions are obtained for posinormality and coposinormality of the operator $D_{\psi,\phi,n}$. Furthermore, the adjoint formula for this operator is derived which also helped us to examine some results regarding posinormality of this operator.

math.FA↗
arXiv2022

Invariant subspaces of idempotents on Hilbert spaces

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed invariant subspace. We also present a geometric characterization of invariant subspaces of idempotents and classify operators that are essentially idempotent.

math.FA↗
arXiv2017

Coefficient Estimates for Certain Subclass of Analytic Functions Defined by Subordination

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with some open problems proposed by Q.H. Xu et al. [20,21]. An application of Jack lemma for certain subclass of starlike functions has been discussed.

math.CV↗
arXiv2016

On Some Subclass of Harmonic Close-to-convex Mappings

Let $\mathcal{H}$ denote the class of harmonic functions $f$ in $\mathbb{D}:= \{z\in \mathbb{C}:|z| < 1\}$ normalized by $f(0) = 0 = f_z(0) -1$. For $α\geq 0$, we consider the following class $$\mathcal{W}^0_{\mathcal{H}}(α):= \{f = h + \overline{g}\in\mathcal{H}: {\rm Re\,}(h'(z) + αz h''(z)) >|g'(z) + αz g''(z)|, \quad z\in \mathbb{D}\}. $$ In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for functions in the class $\mathcal{W}^0_{\mathcal{H}}(α)$. We also prove growth theorem, convolution, convex combination properties for functions in the class $\mathcal{W}^0_{\mathcal{H}}(α)$. Finally, we determine the value of $r$ so that the partial sums of functions in the class $\mathcal{W}^0_{\mathcal{H}}(α)$ are close-to-convex in $|z|<r$.

math.CV↗