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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…

Complex Variables · Mathematics 2021-03-30 Gang Liu , Saminathan Ponnusamy

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…

Complex Variables · Mathematics 2025-07-04 Sabir Ahammed , Molla Basir Ahamed

The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…

Complex Variables · Mathematics 2020-03-13 Bappaditya Bhowmik , Nilanjan Das

In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}$ in the unit disk. Later, we establish the Bohr-type operator on analytic functions…

Complex Variables · Mathematics 2021-04-23 Yong Huang , Ming-Sheng Liu , Saminathan Ponnusamy

In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical…

Complex Variables · Mathematics 2021-01-12 Bappaditya Bhowmik , Nilanjan Das

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…

Complex Variables · Mathematics 2021-05-19 Kamaljeet Gangania , S. Sivaprasad Kumar

The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in…

Functional Analysis · Mathematics 2019-02-26 A. R. Mirotin

In this article, some Bohr inequalities for analytical functions on the unit disk are generalized to the forms with two parameters. One of our results is sharp.

Complex Variables · Mathematics 2025-08-12 Jianying Zhou , Qihan Wang , Boyong Long

Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the Bohr inequality for slice starlike functions and slice…

Complex Variables · Mathematics 2025-11-18 Sabir Ahammed , Molla Basir Ahamed , Ming-Sheng Liu

We say that a class $\mathcal{F}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if there exists $r_{f} \in (0,1)$ such that $$…

Complex Variables · Mathematics 2020-06-30 Vasudevarao Allu , Himadri Halder

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…

Complex Variables · Mathematics 2021-03-25 Saminathan Ponnusamy , Ramakrishnan Vijayakumar , Karl-Joachim Wirths

In this article, we establish the Bohr inequalities for the sense-preserving $K$-quasiconformal harmonic mappings defined in the unit disk $\mathbb{D}$ involving classes of Ma-Minda starlike and convex univalent functions, usually denoted…

Complex Variables · Mathematics 2021-10-26 Kamaljeet Gangania

This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on a sector; here $F$ is given as the Fourier--Borel transform of an analytic functional. The…

Functional Analysis · Mathematics 2018-01-12 I. Chalendar , J. Esterle , J. R. Partington

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series…

Complex Variables · Mathematics 2023-02-16 Kaixin Chen , Ming-Sheng Liu , Saminathan Ponnusamy

Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, %as applications of these results, we obtain several new…

Complex Variables · Mathematics 2024-09-17 Shanshan Jia , Ming-Sheng Liu , Saminathan Ponnusamy

The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A…

Metric Geometry · Mathematics 2026-05-12 Fernanda M. Baêta , Xiaxing Cai

In the present work, we propose to investigate the Fekete-Szeg\"o inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known…

Complex Variables · Mathematics 2014-04-04 Halit Orhan , N. Magesh , V. K. Balaji

In the present investigation, certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szeg\"o functional for functions belonging to the class, distortion, growth estimates and…

Complex Variables · Mathematics 2011-12-30 Nak Eun Cho , Oh Sang Kwon , V. Ravichandran

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…

Complex Variables · Mathematics 2022-08-02 Kamaljeet Gangania

We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the…

Functional Analysis · Mathematics 2021-05-12 Charles Batty , Alexander Gomilko , Yuri Tomilov