Related papers: H\"older's inequality: some recent and unexpected …
In this work, using the well-known mean-value theorem (Lagrange's theorem) we obtain an inequality for n-th order differential equations with retarded argument. If the retarded argument vanishes then the inequality turns to an inequality…
Pointwise H\"older exponents describe the degree of regularity of a function near a point. For a function $f:\mathbb{R}\to\mathbb{R}$, a number $\alpha>0$ and a point $t_0\in\mathbb{R}$, write $f\in C^\alpha(t_0)$ if there is a constant $C$…
In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical…
In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…
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…
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…
We investigate a connection between solvability of the Dirichlet problem for an infinitely degenerate elliptic operator and the validity of an Orlicz-Sobolev inequality in the associated subunit metric space. For subelliptic operators it is…
We formulate and prove a generalization of Hardy's inequality (Hardy,1925) in terms of random variables and show that it contains the usual (or familiar) continuous and discrete forms of Hardy's inequality. Next we improve the recent…
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
In this paper, we derive some new combinatorial inequalities by applying well known real analytic results like H\"{o}lder's inequality, Young's inequality, and Minkowiski's inequality to the recursively defined sequence $f_n$ of functions…
In this paper, we achieve new and improved numerical radius inequalities of operators defined on a Hilbert space by using Orlicz function and Hermite-Hadamard inequality. The upper bounds of various inequalities involving numerical radii…
In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…
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…
In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if…
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…
In my 2011 Annals of Applied Statistics article [Goerg (2011)] I wrote that "Whereas the Lambert $W$ function plays an important role in mathematics, physics, chemistry, biology and other fields, it has not yet been used in statistics."…
By using the vector-valued theory of singular integrals, we prove a Hardy--Littlewood--Sobolev inequality on product Hardy spaces $H^p_{\rm{prod}}$, which is a parallel result of the classical Hardy--Littlewood--Sobolev inequality. The same…
The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…