Related papers: Revisiting Ostrowski's Inequality
In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pe{\l}czy\'nski-type result -- originally established by the first and third authors for $L^p$…
We investigate several possibilities of obtaining a {\L}ojasiewicz inequality for definable multifunctions and give some examples of applications thereof. In particular, we prove that the Hausdorff distance and its extension to closed sets…
Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D.S. Mitrinovic, who left us 25 years ago. His significant influence to…
An inequality providing some bounds for the integral mean via Pompeiu's mean value theorem and applications for quadrature rules and special means are given.
Ostrovskii's generalization of the Marcinkiewicz theorem implies that if an entire characteristic functions of a probability distribution satisfies $\log^+\log|f(z)|=o(|z|),\; z\to\infty,$ and is zero-free then the distribution is normal.…
Carbery proposed the following sharpened form of triangle inequality for many functions: for any $p\ge 2$ and any finite sequence $(f_j)_j\subset L^p$ we have \[ \Big\|\sum_j f_j\Big\|_p \ \le\ \left(\sup_{j} \sum_{k}…
We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on $\ell^r$-valued extensions of linear operators. We show that for certain $1 \leq p, q_1, \dots, q_m, r \leq \infty$, there is a constant $C\geq 0$…
A companion of Ostrowski like inequality for mappings whose second derivatives belong to $L^{\infty}$ spaces is established. Applications to composite quadrature rules, and to probability density functions are also given.
This paper studies a large class of continuous functions $f:[0,1]\to\mathbb{R}^d$ whose range is the attractor of an iterated function system $\{S_1,\dots,S_{m}\}$ consisting of similitudes. This class includes such classical examples as…
The purpose of this paper is to investigate the local and global comparison of two $n$-variable generalized Bajraktarevi\'c means, i.e., to establish necessary as well as sufficient conditions in terms of the unknown functions…
Some sufficient conditions on certain constants which are involved in some first, second and third order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential…
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
The principal aim of this paper is to employ Bessel-type operators in proving the inequality \begin{align*} \int_0^\pi dx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^\pi dx \, \dfrac{|f(x)|^2}{\sin^2 (x)}+\dfrac{1}{4}\int_0^\pi dx \,…
The known Ozaki's condition says that $\mathfrak{Re}\left\{f^{(p)}(z)\right\}>0$ for $|z|<1$ implies that $f(z)=z^p+a_{p+1}z^{p+1}+\cdots$ is at most $p$-valent in $\mathbb D$. In this paper prove an extension of Ozaki's condition. Also, we…
A new weighted Hardy-type inequality for functions from the Sobolev space $W_{p}^{1}$ is proved. It is assumed that functions vanish on small alternating pieces of the boundary. The proved inequality generalizes the classical known weighted…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
In this work we establish functional asymmetric versions of the celebrated Blaschke-Santal\'o inequality. As consequences of these inequalities we recover their geometric counterparts with equality cases, as well as, another inequality with…
The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…
Talenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation…