Related papers: Variational Inequalities For The Differences Of Av…

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm…

Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators.…

In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature the focus of our approach is not testing the null…

Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…

In this paper we show discrepancy bounds for index-transformed uniformly distributed sequences. From a general result we deduce very tight lower and upper bounds on the discrepancy of index-transformed van der Corput-, Halton-, and…

We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…

We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…

We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.

Let $\phi\in \mathscr{S}$ with $\int\phi (x)\, dx=1$, and define $$\phi_t(x)=\frac{1}{t^n}\phi (\frac{x}{t}),$$ and denote the function family $\{\phi_t\ast f(x)\}_{t>0}$ by $\Phi\ast f(x)$. Suppose that there exists a constant $C_1$ such…

We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…

We consider the averages of a function $ f$ on $ \mathbb R ^{n}$ over spheres of radius $ 0< r< \infty $ given by $ A_{r} f (x) = \int_{\mathbb S ^{n-1}} f (x-r y) \; d \sigma (y)$, where $ \sigma $ is the normalized rotation invariant…

Let $\Omega $ be any set of directions (unit vectors) on the plane. We study maximal operators defined by \md0 M_\Omega f(x)=\sup_{\delta >0, \omega \in \Omega} \frac{1}{2\delta}\int_{-\delta}^\delta |f(x+t\omega)|dt. \emd for the…

We discuss some conjectural inequalities that are related to singular integrals, martingales, quasiconformal mappings, and the calculus of variations. Specifically, we present evidence for a conjecture of Iwaniec concerning the best…

There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is…

We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.e. Integral condition is only slightly larger than what the…

In this paper we study a system of variational inequalities where the operator is non-local, possibly degenerate and of second order. A special case of this type of problem occurs in the context of optimal switching problems when the…

Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize the validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt…