Related papers: Bohr radius for invariant families of bounded anal…
Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded…
Let $ \mathcal{H}(\mathbb{D}) $ be the class of analytic functions in the unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $. The classical Bohr's inequality states that if a power series $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ converges in…
The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on…
Based on improving the classical Bohr inequality, we get in this paper some refined versions for a quasi-subordination family of functions, one of which is key to build our results. By means of these investigations, for a family of harmonic…
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 this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
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} :…
We determine the Bohr radius for the class of odd functions $f$ satisfying $|f(z)|\le 1$ for all $|z|<1$, settling the recent conjecture of Ali, Barnard and Solynin \cite{AliBarSoly}. In fact, we solve this problem in a more general…
We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…
This paper mainly uses the nonnegative continuous function $\{\zeta_n(r)\}_{n=0}^{\infty}$ to redefine the Bohr radius for the class of analytic functions satisfying $\real f(z)<1$ in the unit disk $|z|<1$ and redefine the Bohr radius of…
The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$…
The Bohr radius for an arbitrary class $\mathcal{F}$ of analytic functions of the form $f(z)=\sum_{n=0}^{\infty}a_nz^n$ on the unit disk $\mathbb{D}=\{z\in\mathbb{C} : |z|<1\}$ is the largest radius $R_{\mathcal{F}}$ such that every…
In this paper we first consider another version of the Rogosinski inequality for analytic functions $f(z)=\sum_{n=0}^\infty a_nz^n$ in the unit disk $|z| < 1$, in which we replace the coefficients $a_n$ $(n= 0,1,\ldots ,N)$ of the power…
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination family of functions, and establish the classical Bohr's inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain…
In this article, we determine sharp Bohr-type radii for certain complex integral operators defined on a set of bounded analytic functions in the unit disk.
The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find…
In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the…
This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{D}^n$. We establish a sharp extension of the classical Bohr…
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…
In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in $\mathbb{C}^n$ under some restricted conditions. Next, we determine the refined version of…