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Vibhuti Arora

Publications and source records attributed to Vibhuti Arora.

11 recordsLinked to original sources
arXiv2025

Estimates of the Second Bohr radius for vector-valued Holomorphic functions

This paper introduces the second Bohr radius for vector-valued holomorphic functions defined on arbitrary complete Reinhardt domains. We aim to establish the lower and upper bounds of the second Bohr radius in both finite and infinite-dimensional settings. Additionally, we provide specific estimates that connect the Second Bohr radius to a symmetric Banach space. We also explore the relationships between our findings and certain existing results.

math.CV↗
arXiv2025

Schwarz-Pick type lemma and Landau type theorem for $α$-harmonic mappings

The aim of this paper is twofold. First, we obtain a Schwarz-Pick type lemma for the $α$-harmonic mapping $u=P_α[ϕ]$, where $ϕ\in L^{p}(\mathbb{S}^{n-1},\mathbb{R} )$ and $p\in[1,\infty]$. We get an explicit form of the sharp function $\mathbf{C}_{α, q}(x)$ in the inequality $|\nabla u(x)| \leq \mathbf{C}_{α, q}(x)\|ϕ\|_{L^p(\mathbb{S}^{n-1}, \mathbb{ R} )}$. Second, we prove a Landau type theorem for $u=P_α[ϕ]$, where $ϕ\in L^{\infty}(\mathbb{S}^{n-1},\mathbb{R}^{n})$. These results generalize and extend the corresponding results due to Kalaj (Complex Anal. Oper. Theory, 2024) and Khalfallah et al. (Mediterr. J. Math., 2021).

math.AP↗
arXiv2025

Revisit Of Meromorphic Convex Functions

Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $α$, where $0 \leq α< 1$. The investigation will focus on studying a class of continuous functions defined on $[0,1)$, and analyzing the properties of the Schwarzian norm of locally univalent meromorphic functions. Moreover, a new subclass of meromorphic functions is also introduced, and some of its characteristics are examined.

math.CV↗
arXiv2024

Asymptotic value of the multidimensional Bohr radius

This article determines the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the $\ell_p^n$ space and having values in the simply connected domain of $\mathbb{C}$. Moreover, we investigate sharp Bohr radius for four distinct categories of holomorphic functions. These functions map the bounded balanced domain $G$ of a complex Banach space $X$ into the following domains: the right half-plane, the slit domain, the punctured unit disk, and the exterior of the closed unit disk.

math.CV↗
arXiv2022

Bohr-Rogosinski type inequalities for concave univalent functions

In this paper, we generalize and investigate Bohr-Rogosinski's inequalities and the Bohr-Rogosinski phenomenon for the subfamilies of univalent (i.e., one-to-one) functions defined on unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$ which maps to the concave domain, i.e., the domain whose complement is a convex set. All the results are proved to be sharp.

math.CV↗
arXiv2021

Initial Successive coefficients of Inverse functions of certain classes of univalent functions

We consider functions of the type $f(z)=z+a_2z^2+a_3z^3+\cdots$ from a family of all analytic and univalent functions in the unit disk. Let $F$ be the inverse function of $f$, given by $F(z)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some $|w|\le r_0(f)$. In this paper, we find the sharp bounds of $\big | |A_{n+1}|-|A_n|\big |$, for $n=1,\,2$, for some subclasses of univalent functions.

math.CV↗
arXiv2021

Initial successive coefficients for certain classes of univalent functions

We consider a family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients, i.e. $\big | |a_{n+1}|-|a_n|\big |$ for $n=1,\,2$ and for some subclasses of analytic univalent functions. We found that all the estimations are sharp in nature by constructing some extremal functions.

math.CV↗
arXiv2019

Successive coefficients for spirallike and related functions

We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big | |a_{n+1}|-|a_n|\big |$, for $f$ belonging to the family of $γ$-spirallike functions of order $α$. Our particular results include the case of starlike and convex functions of order $α$ and other related class of functions.

math.CV↗
arXiv2017

Meromorphic functions with small Schwarzian derivative

We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\frac{1}{z}+b_0+b_1z+b_2z^2+\cdots $$ analytic and locally univalent in the puncture disk $\mathbb{D}_0:=\{z\in\mathbb{C}:\,0<|z|<1\}$. Our first objective in this paper is to find a sufficient condition for $f$ to be meromorphically convex of order $α$, $0\le α<1$, in terms of the fact that the absolute value of the well-known Schwarzian derivative $S_f (z)$ of $f$ is bounded above by a smallest positive root of a non-linear equation. Secondly, we consider a family of functions $g$ of the form $g(z)=z+a_2z^2+a_3z^3+\cdots$ analytic and locally univalent in the open unit disk $\mathbb{D}:=\{z\in\mathbb{C}:\,|z|<1\}$, and show that $g$ is belonging to a family of functions convex in one direction if $|S_g(z)|$ is bounded above by a small positive constant depending on the second coefficient $a_2$. In particular, we show that such functions $g$ are also contained in the starlike and close-to-convex family.

math.CV↗