Related papers: Bohr-Rogosinski Inequalities for bounded analytic …
In this paper, we first determine Bohr's inequality for the class of harmonic mappings $f=h+\overline{g}$ in the unit disk $\ID$, where either both $h(z)=\sum_{n=0}^{\infty}a_{pn+m}z^{pn+m}$ and $g(z)=\sum_{n=0}^{\infty}b_{pn+m}z^{pn+m}$…
In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \begin{equation*} \Omega_{\gamma}=\bigg\{z\in\mathbb{C} :…
In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $\Omega$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the…
Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…
In this article, we study the Bohr type inequality for {C}es\'{a}ro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.
In this paper, we study the Bohr phenomenon for differential operators $D$ and $\mathscr{D}$ of stable harmonic mappings involving multiple Schwarz functions in $\mathcal{B}_n$, using distance formulations. By constructing suitable…
Let $ \mathcal{H}(\mathbb{D}) $ be the linear space of analytic functions on the unit disk $ \mathbb{D}=\{z\in\mathbb{C}: |z|<1\} $ and let $ \mathcal{B}=\{w\in \mathcal{H}(\mathbb{D}: |w(z)|<1)\} $. The classical Bohr's inequality states…
In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we…
The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality…
We say that a class $\mathcal{B}$ of analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if for the largest radius $R_{f}<1$, the…
A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…
Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…
The concept of Bohr radius for the class of bounded analytic functions was introduced by Harald Bohr in 1914. His initial result received greater interest and was sharpened-refined-generalized by several mathematicians in various…
The classical Bohr theorem and its subsequent generalizations have become active areas of research, with investigations conducted in numerous function spaces. Let $\{\psi_n(r)\}_{n=0}^\infty$ be a sequence of non-negative continuous…
In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved Bohr inequality with a certain power of the norm of the…
For $f(z) = \sum_{n=0}^{\infty} a_n z^n$ and a fixed $z$ in the unit disk, $|z| = r,$ the Bohr operator $\mathcal{M}_r$ is given by \[\mathcal{M}_r (f) = \sum_{n=0}^{\infty} |a_n| |z^n| = \sum_{n=0}^{\infty} |a_n| r^n.\] This papers…
In this paper, we derive the sharp Bohr type inequality for the Ces\'aro operator, Bernardi integral operator, and discrete Fourier transform acting on the class of bounded analytic functions defined on shifted disks \beas…
In Geometric function theory, occasionally attempts have been made to solve a particular problem for the Ma-Minda classes, $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of univalent starlike and convex functions, respectively. Recently, a…
In this article we prove Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings defined in $\mathbb{D}$ and obtain the corresponding results for sense-preserving harmonic mappings by letting $K\to\infty$. One of the…
Let $\phi$ be analytic and univalent ({\it i.e.,} one-to-one) in $\mathbb{D}:=\{z\in\mathbb{C}: |z|<1\}$ such that $\phi(\mathbb{D})$ has positive real part, is symmetric with respect to the real axis, starlike with respect to $\phi(0)=1,$…