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The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions…

Complex Variables · Mathematics 2021-10-05 Shaolin Chen , Hidetaka Hamada

We prove the stronger version of Harnack's inequality for positive harmonic functions defined on the unit disc.

Complex Variables · Mathematics 2025-01-20 Marek Svetlik

In this article, we study Bohr-type inequalities involving a parameter or convex combinations for $K$-quasiconformal, sense-preserving harmonic mappings in $\mathbb{D}$, where the analytic part is subordinate to a convex function. Moreover,…

Complex Variables · Mathematics 2025-09-11 Molla Basir Ahamed , Taimur Rahman

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $\mathcal{B}$, which consists of analytic self-mappings defined on the unit disk $\mathbb{D}$. We improve the Bohr-Rogosinski…

Complex Variables · Mathematics 2025-12-19 Molla Basir Aahmed , Partha Pratim Roy

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

Complex Variables · Mathematics 2019-05-07 See Keong Lee , Saminathan Ponnusamy , Karl-Joachim Wirths

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

Complex Variables · Mathematics 2025-12-09 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar , Ming-Sheng Liu

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…

Complex Variables · Mathematics 2017-08-21 Ilgiz R Kayumov , Saminathan Ponnusamy

In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…

Complex Variables · Mathematics 2021-04-14 Ramakrishnan Vijayakumar

Recently, there has been a number of good deal of research on the Bohr's phenomenon in various setting including a refined formulation of his classical version of the inequality. Among them, in \cite{PaulPopeSingh-02-10} the authors…

Complex Variables · Mathematics 2020-06-12 Saminathan Ponnusamy , Karl-Joachim Wirths

We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon…

Functional Analysis · Mathematics 2020-11-26 Bappaditya Bhowmik , Nilanjan Das

In this paper, we define certain subclass of harmonic univalent function in the unit disc U = {z in C :|z|<1} by using q-differential operator. Also we obtain coefficient inequalities, growth and distortion theorems for this subclass.

Complex Variables · Mathematics 2022-09-13 G. M. Birajdar , N. D. Sangle

In this paper, the author established Hermite-Hadamard's inequalities for harmonically convex functions via fractional integrals and obtained some Hermite-Hadamard type inequalities of these classes of functions.

Classical Analysis and ODEs · Mathematics 2013-12-30 Imdat Iscan

Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.

Functional Analysis · Mathematics 2026-01-16 Anca Croitoru , Alina Iosif , Anna Rita Sambucini , Luca Zampogni

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

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…

Functional Analysis · Mathematics 2022-01-26 Vern I. Paulsen , Dinesh Singh

The author introduce the concept of harmonically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions

Classical Analysis and ODEs · Mathematics 2013-03-26 Imdat Iscan

We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…

Functional Analysis · Mathematics 2011-07-08 Masatoshi Fujii , Mohammad Sal Moslehian , Jadranka Micic

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 $\phi(0)=1,$…

Complex Variables · Mathematics 2026-04-15 Vasudevarao Allu , Himadri Halder

We study noncommutative versions of holomorphic and harmonic functions on the unit disk.

Operator Algebras · Mathematics 2007-05-23 Slawomir Klimek

A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…

Complex Variables · Mathematics 2012-07-17 Sumit Nagpal , V. Ravichandran