Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.13869

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

Sujoy Majumder·Abhijit Banerjee·Goutam Haldar
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sujoy Majumder, Abhijit Banerjee, Goutam Haldar. 2026-10-09. Sharp Robertson-type coefficient estimates for radial starlike and quasi-convex of type B mappings of order α in complex Banach spaces. https://arxiv.org/abs/2610.13869

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Absolute moments of GH distribution

In this work, we focus on deriving the absolute moments of the general ized hyperbolic (GH) distribution via its mean-variance mixture structure. Conditioning on the GIG mixing variable reduces the problem to Gaussian moment calculations and known GIG power moments, avoiding direct integration with Bessel functions. The variance gamma (VG), normal inverse Gaussian (NIG), hyperbolic, Normal, and Student t distributions emerge as natural special or limiting cases of the generalized hyperbolic family. This approach offers a substantially simpler and more transparent derivation, facilitating both implementation and verification.

math.CV↗
arXiv2026

A universal $\overline\partial$ solution operator on nonsmooth strongly pseudoconvex domains

We construct a universal family of $\overline\partial$ homotopy operators on bounded $C^{1,1}$ domains that are locally strongly $\mathbb C$-linearly convexifiable. In particular this includes $C^2$ strongly pseudoconvex domains and $C^{1,1}$ strongly $\mathbb C$-linearly convex domains. The operators satisfy Sobolev estimates $\mathcal H_q:H^{s,p}\to H^{s+1/2,p}$ and Hölder-Zygmund estimates $\mathcal H_q:\mathscr C^s\to\mathscr C^{s+1/2}$ simultaneously for all $s\in\mathbb R$ and $1<p<\infty$. The construction uses a modification of the Leray-Koppelman formula and a refined directional decomposition of the commutator $[\overline\partial,\mathcal E]$.

math.CV↗
arXiv2026

The Carathéodory metric on Teichmüller space of genus two surface

Let $\Tei_{g,n}$ be the Teichmüller space of Riemann surfaces of genus $g$ with $n$ marked points. It is conjectured that the Teichmüller and Carathéodory metrics coincide on a Teichmüller disk exactly when every zero of the associated holomorphic quadratic differential (away from marked points) has even order. Gekhtman and Markovic verified this conjecture for $\Tei_{0,5}\cong \Tei_{1,2}$. We confirm the conjecture for $\Tei_{0,6}\cong\Tei_{2,0}$.

math.CV↗