arXiv subjects

Pradip Das

Publications and source records attributed to Pradip Das.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Bounds for Higher-Order Schippers Functionals Associated with Lune and Bean Domains

We obtain sharp bounds for the third- and fourth-order Schippers functionals, $|\sigma_3(f)(0)|$ and $|\sigma_4(f)(0)|$, for subclasses of univalent functions associated with non-classical geometric domains. In particular, we investigate the lune-starlike class $\mathcal{S}_{\leftmoon}^*$ and the lune-convex class $\mathcal{C}_{\leftmoon}$ determined by the subordination \[ \frac{zf'(z)}{f(z)} \prec z+\sqrt{1+z^2}, \qquad 1+\frac{zf''(z)}{f'(z)} \prec z+\sqrt{1+z^2}, \] respectively, together with the bean-domain class $\mathcal{BT}_{\mathfrak{B}}$ associated with \[ \mathfrak{B}(z)=\sqrt{1+\tanh z}. \] Using Carath\'eodory coefficient parametrizations and extremal optimization techniques, we derive exact estimates for the higher-order Schwarzian derivatives at the origin and identify the corresponding extremal functions. In addition, geometric descriptions of the associated extremal image domains are provided to illustrate the sharpness phenomena. The obtained results further yield sharp bounds for the initial Grunsky coefficients $g_{1,1}$ and $g_{1,2}$. These findings provide a precise description of higher-order Schwarzian structures for univalent functions related to lune- and bean-shaped domains.

math.CV↗

arXiv2026

Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class $\mathcal{S}_{car}^*$

This paper focuses on coefficient problems for the class of starlike functions related to a cardioid region. We derive sharp bounds for the Hankel determinants of logarithmic coefficients and logarithmic inverse coefficients of order two. Additionally, we completely solve the extremal problem for the third-order Hermitian--Toeplitz determinant by providing its sharp upper and lower bounds. All results are supported by extremal examples demonstrating the sharpness of the obtained estimates.

math.CV↗

arXiv2026

Second Hankel Determinant for $\beta$-Spirallike Convex Mappings in Complex Banach Spaces

We establish the bound for the second-order Hankel determinant $H_{2,2}(F) = A_2 A_4 - A_3^2$ associated with the class $\mathcal{C}_{B}^{\beta}(\mathbb{B})$ of normalized $\beta$-spirallike quasi-convex mappings of type $B$ on the open unit ball $\mathbb{B}$ of a complex Banach space. By utilizing a generalized framework based on a directional slice homogeneous polynomial expansion, we eliminate the standard, restrictive assumption that the mapping is of the form $F(x) = g(x)x$. Under these weaker operational conditions, we parameterize the targeted scalar invariants $A_n$ via the classical Carath\'{e}odory functional parameters. A rigorous optimization analysis proves that the established upper bound is strictly sharp for the classical non-spirallike case $\beta = 0$, yielding a maximal value of $1/8$. This sharp bound is verified by constructing explicit multi-dimensional extremal mappings that lift the corresponding single-variable convex profile. Finally, an unresolved open question regarding the exact variational behavior for $\beta \neq 0$ is formulated.

math.CV↗

arXiv2026

Bohr-type inequalities with Fr\'{e}chet derivative and Area terms in Complex Banach spaces

We establish new Bohr-type inequalities for holomorphic mappings from the unit ball of a complex Banach space into the closed unit disk. Using Fr\'{e}chet derivatives, Schwarz mappings of prescribed orders and area functionals, we obtain sharp Bohr radii characterized by explicit equations. We further prove a refined Bohr inequality involving derivative, coefficient and area terms and show that the corresponding radius is the unique positive solution of $r^m=(\sqrt{17}-3)/4$. The sharpness of the obtained radii and constants is also established. Our results extend several recent Bohr-type inequalities for bounded analytic functions on the unit disk to the setting of holomorphic mappings on complex Banach spaces.

math.CV↗

arXiv2026

Improved Bohr inequalities involving Fr\'{e}chet derivatives associated with Holomorphic mappings in Banach spaces

Motivated by recent advances in derivative Bohr inequalities and their refinements, we investigate the Bohr phenomenon for holomorphic mappings in complex Banach spaces associated with Schwarz functions. We establish sharp Bohr-type inequalities involving higher-order Fr\'{e}chet derivatives for both $|F(z)|$ and its refined counterpart $|F(z)|^2$. The corresponding Bohr radii are determined and shown to be best possible. Our results provide affirmative answers to Questions 1.1 and 1.2 and extend several classical and recent Bohr inequalities from the unit disk to the setting of holomorphic mappings on Banach spaces.

math.CV↗

arXiv2026

Coefficient Problems and Sharp Determinant Estimates for the Class $\mathcal{P}^{*}$

We study coefficient problems for the class $\mathcal{P}^{*}$ of normalized analytic functions $f$ in the unit disk satisfying the subordination condition \[ f'(z) \prec e^z(1+\sin z), \qquad z\in\mathbb{D}. \] For functions in this class, we determine sharp bounds for the logarithmic coefficients $\gamma_n$ for $n=1,2,3,4$ and for the inverse logarithmic coefficients $\Gamma_n$ for $n=1,2,3$. In particular, we prove \[ |\gamma_n| \le \frac{1}{n+1} \quad (n=1,2,3,4), \qquad |\Gamma_1|,|\Gamma_2| \le \frac12,\quad |\Gamma_3|\le \frac{35}{48}, \] with equality cases explicitly identified. Moreover, we establish sharp estimates for the moduli of the differences $|\gamma_2|-|\gamma_1|$ and $|\Gamma_2|-|\Gamma_1|$, yielding \[ -\frac12 \le |\gamma_2|-|\gamma_1| \le \frac13, \qquad -\frac{1}{\sqrt{10}} \le |\Gamma_2|-|\Gamma_1| \le \frac13. \] Turning to determinant problems, we obtain sharp upper bounds for the second-order Hankel determinants associated with both the logarithmic and inverse logarithmic coefficients: \[ \bigl|H_{2,1}(F_f/2)\bigr| \le \frac19,\qquad \bigl|H_{2,1}(F_{f^{-1}}/2)\bigr| \le \frac{11}{96}. \] Finally, we derive the sharp two-sided estimate \[ -\frac{9}{35} \le T_{3,1}(f) \le 1 \] for the third-order Hermitian--Toeplitz determinant. All bounds are sharp, and the extremal functions are given explicitly. Our results extend and refine several known coefficient estimates for related subclasses of starlike and convex functions.

math.CV↗

arXiv2026

Higher-Order Schippers-Schwarzian Derivatives for Non-Circular Starlike Functions

We find sharp upper bounds for the initial higher-order Schippers-Schwarzian derivatives $\sigma_3(f)(0)$ and $\sigma_4(f)(0)$ for several subclasses of univalent and starlike functions in the unit disk. The functions in these classes are defined by subordination to domains bounded by an exponential-sine curve, a cardioid, or a petal-shaped curve. We determine the sharp bounds and find the corresponding extremal functions for each invariant in these subclasses. As an application, we also obtain sharp bounds for the initial Grunsky coefficients $\omega_{1,1}$ and $\omega_{1,2}$.

math.CV↗

arXiv2026

Sharp Estimates for Hankel, Fekete-Szeg\"o and Zalcman Functionals for $\mathcal{S}_\mathbb{B}^{*}(\alpha)$ in Complex Banach Spaces

Inspired by the sharp coefficient estimates established by Cho \emph{et al.}\cite{CKKLS2018} for starlike functions of order $\alpha$ in the unit disk, we investigate the corresponding problems for starlike mappings of order $\alpha$ defined on the unit ball of a complex Banach space. Employing Fr\'echet derivatives together with suitable auxiliary lemmas, we establish sharp upper bounds for the second-order Hankel determinant, the Fekete--Szeg\"o functional, and the Zalcman functional associated with this class of mappings. In each case, the obtained estimates are shown to be sharp by identifying the corresponding extremal mappings. Furthermore, our results reduce to the known one-dimensional sharp estimates when the underlying Banach space is the complex plane, thereby extending several classical results of Cho \emph{et al.} \cite{CKKLS2018} to the setting of complex Banach spaces.

math.CV↗

arXiv2026

On Hankel Determinants of $\beta$-Spirallike Mappings in Complex Banach Spaces

This paper is devoted to the study of the second Hankel determinant for normalized $\beta$-spirallike mappings on the unit ball of a complex Banach space. Using the relationship between Banach-space holomorphic mappings and corresponding one-variable $\beta$-spirallike functions, we first establish sharp estimates for the initial homogeneous expansion coefficients. These coefficient inequalities are subsequently applied to derive a sharp bound for the second Hankel determinant.

math.CV↗

arXiv2026

Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces

In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian--Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to $\mathcal{F}_{O}(\lambda)$.

math.CV↗

arXiv2026

Inverse Logarithmic Coefficients and Associated Sharp Estimates for the Apple-Like Convex Subclass $\mathcal{C}_{\mathcal{AP}}$

This paper addresses coefficient problems for the apple-like convex subclass $\mathcal{C}_{\mathcal{AP}}$, defined by the subordination relation $1+zf''(z)/f'(z) \prec e^z\sqrt{1+z}$. We determine sharp bounds for the initial inverse logarithmic coefficients $\Gamma_1$, $\Gamma_2$, $\Gamma_3$, and the consecutive modulus difference $|\Gamma_2|-|\Gamma_1|$. We also obtain the sharp upper bound for the second-order inverse logarithmic Hankel determinant, characterize the generalized Fekete--Szeg\H{o} functional for all real parameters, and compute sharp bounds for the third-order Hermitian--Toeplitz determinant. Extremal functions are given for each case.

math.CV↗

arXiv2026

Sharp coefficient Estimates for the class $\mathcal{S}_{\mathcal{AP}}^{*}$

We investigate several classic coefficient problems for the Ma--Minda starlike subclass $\mathcal{S}_{\mathcal{AP}}^{*}$ defined by the apple-like subordination function $\psi_{\mathcal{AP}}(z)=e^{z}\sqrt{1+z}$. Sharp bounds are derived for the initial inverse logarithmic coefficients $\Gamma_1$, $\Gamma_2$, $\Gamma_3$, and the successive modulus difference $|\Gamma_2|-|\Gamma_1|$. In addition, we evaluate the second-order inverse logarithmic Hankel determinant, the generalized Fekete--Szeg\"o functional over all real parameter domains, and the third-order Hermitian--Toeplitz determinant. The corresponding extremal functions are explicitly determined for each functional.

math.CV↗

arXiv2026

Sharp Coefficient Estimates for the Exponential Starlike class $\mathcal{S}_{ex}^{\ast}$

Let $\mathcal{S}_{ex}^{\ast}$ denote the class of normalized analytic functions $f$ in the unit disk satisfying \[ \frac{zf'(z)}{f(z)} \prec e^{\alpha z},\qquad 0<\alpha\le 1. \] We obtain sharp bounds for the initial inverse logarithmic coefficients $\Gamma_1$, $\Gamma_2$, and $\Gamma_3$. In particular, the bound for $|\Gamma_3|$ has a four-branch structure with transition values \[ \alpha_\star \approx 0.542712,\qquad \alpha_b \approx 0.679103,\qquad \alpha_c \approx 0.691095. \] We also establish sharp upper and lower bounds for the successive coefficient difference \[ |\Gamma_2|-|\Gamma_1|, \] for the inverse logarithmic Hankel determinant \[ H_{2,1}\bigl(F_{f^{-1}}/2\bigr), \] and for the third-order Hermitian--Toeplitz determinant $T_{3,1}(f)$, whose sharp lower bound changes at \[ \alpha_H=\frac{-1+\sqrt{241}}{15}\approx0.9683. \] Furthermore, we completely solve the sharp generalized Fekete--Szeg\H{o} problem for the functional \[ |a_3-\lambda a_2^2|-\mu|a_2|. \] All estimates are sharp, and the corresponding extremal functions are explicitly constructed by using Carath\'eodory function representations.

math.CV↗

arXiv2026

Inverse Logarithmic Coefficients, Differences, Hankel Determinant, and Fekete--Szeg\"{o} Functionals for the Class $\mathcal{C}_e$

In this paper, we investigate the inverse logarithmic coefficients associated with the class $\mathcal{C}_e$ of analytic and univalent functions satisfying the subordination condition \[ 1+\frac{z f''(z)}{f'(z)} \prec e^z, \quad z\in\mathbb{D}. \] If $F_{f^{-1}}(w) = \log\!\left(\frac{f^{-1}(w)}{w}\right) = 2\sum_{n=1}^{\infty}\Gamma_n w^n$ denotes the logarithmic expansion corresponding to the inverse function $f^{-1}$, then we establish sharp estimates for the initial inverse logarithmic coefficients and prove that \[ |\Gamma_n| \le \frac{1}{2n(n+1)}, \qquad n=1,2,3. \] We further derive the sharp coefficient-difference inequality \[ -\frac{1}{2\sqrt7} \le |\Gamma_2|-|\Gamma_1| \le \frac1{12}, \] and obtain the sharp bound for the second-order Hankel determinant associated with the inverse logarithmic coefficients: \[ \left| H_{2,1}\!\left(F_{f^{-1}}/2\right) \right| \le \frac{85}{12096}. \] Additionally, we evaluate the sharp lower and upper bounds of the generalized Fekete--Szeg\"{o} functional $F_{\lambda, \mu}(f) = \big| a_3(f) - \lambda a_2(f)^2 \big| - \mu |a_2(f)|$ within this setting and establish relationships associated with the starlike class $\mathcal{S}^{\ast}_{\rho}$. The extremal functions corresponding to all obtained estimates are explicitly constructed, thereby showing the sharpness of the results.

math.CV↗

arXiv2024

Endless Dirac nodal lines and high mobility in kagome semimetal Ni3In2Se2 single crystal

Kagome-lattice crystal is crucial in quantum materials research, exhibiting unique transport properties due to its rich band structure and the presence of nodal lines and rings. Here, we investigate the electronic transport properties and perform first-principles calculations for Ni$_{3}$In$_{2}$Se$_{2}$ kagome topological semimetal. First-principle calculations indicate six endless Dirac nodal lines and two nodal rings with a $\pi$-Berry phase in the Ni$_{3}$In$_{2}$Se$_{2}$ compound. The temperature-dependent resistivity is dominated by two scattering mechanisms: $s$-$d$ interband scattering occurs below 50 K, while electron-phonon ($e$-$p$) scattering is observed above 50 K. The magnetoresistance (MR) curve aligns with the theory of extended Kohler's rule, suggesting multiple scattering origins and temperature-dependent carrier densities. A maximum MR of 120\% at 2 K and 9 T, with a maximum estimated mobility of approximately 3000 cm$^{2}$V$^{-1}$s$^{-1}$ are observed. The Ni atom's hole-like d$_{x^{2}-y^{2} }$ and electron-like d$_{z^{2}}$ orbitals exhibit peaks and valleys, forming a local indirect-type band gap near the Fermi level (E$_{F}$). This configuration enhances the motion of electrons and holes, resulting in high mobility and relatively high magnetoresistance.

cond-mat.mtrl-sci↗

arXiv2018

Vibrational Spectra of Pb2Bi2Te3, PbBi2Te4 and PbBi4Te7 Topological Insulators: Temperature Dependent Raman and Theoretical Insight from DFT Simulations

We present temperature dependent frequency shift and line broadening of phonon modes by insertion of atomic layers of Pb and PbTe in the prototype 3D topological insulator Bi2Te3, using Raman spectroscopy. Good quality single crystals of Pb2Bi2Te3, PbBi2Te4 and PbBi4Te7 are grown using the modified Bridgman technique. The Raman modes show progressive blue shift with the decrease in temperature from 298 K to 93 K in Pb2Bi2Te3, PbBi2Te4 and PbBi4Te7 is due to anharmonic vibrations of the lattice as well as increasing strength of Bi-Te covalent interactions. Experimental results are complemented by extensive density functional theory calculations where a reasonable matching between experimental and computational data is found. Chemical pressure, induces by the insertion of Pb and PbTe layers in Bi2Te3, modifies the interactions at the boundaries of the quintuple-layers which is evident from the evolution of mode. The enhancement of out-of-plane Bi-Te vibrations with respect to in-plane Bi-Te vibrations are observed at low temperatures.

cond-mat.mes-hall↗

arXiv2011

Spin-Triplet Vortex State in the Topological Superconductor CuxBi2Se3

We report on the observation of bulk superconductivity from dc magnetization measurements in a cylindrical single crystal of CuxBi2Se3. The magnitude of the magnetization in the Meissner state is very small and the magnetic-field dependence of the magnetization just above the lower critical field Hc1 is very different from those of usual type-II superconductors. We studied the character of the vortex state theoretically in a spin-triplet pairing superconductor and compared it with the experimental results. The results showed that, the superconductivity observed in CuxBi2Se3 is consistent with the spin-triplet pairing superconductivity with odd parity. We also observed a rapid relaxation phenomenon of the superconducting diamagnetism.

cond-mat.supr-con↗

arXiv2008

Anisotropy in vortex phase diagram and the pinning force density in the basal plane of YNi_2B_2C

We present magnetic field dependence of the critical current density from dc-magnetization measurements concerning the anisotropic behavior of flux line lattice (FLL) in a single crystal of YNi_2B_2C. The peak effect (PE) phenomenon is observed for all crystallographic orientations, but the second magnetization peak (SMP) anomaly is observed only for H//a. Our study reveals that the FLL obtained when H//[100] is better ordered within the basal plane. However, the FLL for H// c is found to be even more ordered than that for H//[110]. The perfect square symmetry of the FLL for H//c is perhaps responsible for promoting the realization of the best spatial order of the FLL prior to the onset of PE, indicating a correlation between the crystalline lattice and the FLL. We have also found a change over in the power law governing the decay of the critical current density which is identified as a crossover from weak to weaker pinning regime in the phase diagram.

cond-mat.supr-con↗