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In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

Complex Variables · Mathematics 2019-04-25 I. R. Kayumov , K. -J. Wirths

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

Complex Variables · Mathematics 2025-02-06 Wanqing Hou , Qihan Wang , Boyong Long

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 primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic…

Complex Variables · Mathematics 2026-04-14 Raju Biswas , Rajib Mandal

In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain…

Complex Variables · Mathematics 2024-06-21 Prachi Prajna Dash , Jugal Kishore Prajapat

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…

Complex Variables · Mathematics 2020-12-14 Molla Basir Ahamed , Vasudevarao Allu , Himadri Halder

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…

Complex Variables · Mathematics 2025-11-25 Vasudevarao Allu , Raju Biswas , Rajib Mandal

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…

Complex Variables · Mathematics 2020-04-21 Seraj A. Alkhaleefah , Ilgiz R. Kayumov , Saminathan Ponnusamy

A class $ \mathcal{F} $ consisting of analytic functions $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ in the unit disc $ \mathbb{D}=\{z\in\mathbb{C}:|z|<1\} $ satisfies a Bohr phenomenon if there exists an $ r_f>0 $ such that \begin{equation*}…

Complex Variables · Mathematics 2022-12-13 Molla Basir Ahamed

In this paper, some Hermite-Hadamard type inequalities are established for harmonically $(\alpha,m)$-convex functions via fractional integrals and some Hermite-Hadamard type inequalities are obtained for these classes of functions.

Classical Analysis and ODEs · Mathematics 2015-05-12 Mehmet Kunt , İmdat İşcan

We prove several improved versions of Bohr's inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $|g'(z)|\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov…

Complex Variables · Mathematics 2017-09-27 Stavros Evdoridis , Saminathan Ponnusamy , Antti Rasila

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…

Complex Variables · Mathematics 2025-11-17 Sujoy Majumder , Nabadwip Sarkar , Molla Basir Ahamed

In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are…

Complex Variables · Mathematics 2019-01-25 Adnan Ghazy AlAmoush

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…

Complex Variables · Mathematics 2026-04-14 Raju Biswas , Rajib Mandal

In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.

Classical Analysis and ODEs · Mathematics 2012-03-13 Mehmet Zeki Sarikaya , Hatice Yaldiz , Hakan Bozkurt

Let $ \mathcal{H}(\Omega) $ be the class of complex-valued functions harmonic in $ \Omega\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(\Omega)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain…

Complex Variables · Mathematics 2024-02-20 Molla Basir Ahamed , Partha Pratim Roy

In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace…

Complex Variables · Mathematics 2024-05-08 Molla Basir Ahamed , Partha Pratim Roy , Sabir Ahammed

A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.

Classical Analysis and ODEs · Mathematics 2007-05-23 Yifei Pan , Mei Wang

In this paper, we study Bohr's inequality and refined versions of Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we establish a version of multidimensional analogue of Bohr inequality and Bohr-Rogosinski inequalities…

Complex Variables · Mathematics 2023-12-12 Sabir Ahammed , Molla Basir Ahamed

In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.

Differential Geometry · Mathematics 2025-06-23 Gianluca Bande