Related papers: Strong convergence for the modified Mann's iterati…
We show that for a fixed integer $n \neq \pm2$, the congruence $x^2 + nx \pm 1 \equiv 0 \pmod{\alpha}$ has the solution $\beta$ with $0 < \beta < \alpha$ if and only if $\alpha/\beta$ has a continued fraction expansion with sequence of…
We introduce a call-by-name lambda-calculus $\lambda Jn$ with generalized applications which is equipped with distant reduction. This allows to unblock $\beta$-redexes without resorting to the standard permutative conversions of generalized…
Given $d \ge 1$, let $(A_i)_{i\ge 1}$ be a sequence of random $d\times d$ real matrices and $Q$ be a random vector in $\mathbb{R}^d$. We consider fixed points of multivariate smoothing transforms, i.e. random variables $X\in \mathbb{R}^d$…
Let $(X,\|.\|)$ be a Banach space. Let $C$ be a nonempty, bounded, closed, and convex subset of $X$ and $T: C \rightarrow C$ be a $G$-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by…
We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…
In this paper, we present a very accurate approximation for gamma function: \begin{equation*} \Gamma \left( x+1\right) \thicksim \sqrt{2\pi x}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \frac{1}{x}\right) ^{x/2}\exp \left(…
We show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Panyanak and the Tikhonov-Mann iteration introduced by H. Cheval…
We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…
We study the $\Gamma$-convergence of the functionals $F_n(u):= || f(\cdot,u(\cdot),Du(\cdot))||_{p_n(\cdot)}$ and $\mathcal{F}_n(u):= \int_{\Omega} \frac{1}{p_n(x)} f^{p_n(x)}(x,u(x),Du(x))dx$ defined on $X\in \{L^1(\Omega,\mathbb{R}^d),…
The aim of this paper is to investigate strong convergence of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to…
We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…
We prove for any mu = mu^{< mu}< theta < lambda, lambda large enough (just strongly inaccessible Mahlo) the consistency of 2^mu = lambda-> [theta]^2_3 and even 2^mu = lambda-> [theta]^2_{sigma,2} for sigma < mu . The new point is that…
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…
Let $\beta\equiv\beta^{(2n)}$ be an N-dimensional real multi-sequence of degree 2n, with associated moment matrix $\mathcal{M}(n)\equiv \mathcal{M}(n)(\beta)$, and let $r:=rank \mathcal{M}(n)$. We prove that if $\mathcal{M}(n)$ is positive…
We look for a parallel to the notion of ``proper forcing'' among lambda-complete forcing notions not collapsing lambda^+ . We suggest such a definition and prove that it is preserved by suitable iterations.
We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple…
Let $\lambda \in (0,1)$ and let $T$ be a $r\times r$ complex matrix with polar decomposition $T=U|T|$. Then, the $\la$- Aluthge transform is defined by $$ \Delta_\lambda (T )= |T|^{\lambda} U |T |^{1-\lambda}. $$ Let $\Delta_\lambda^{n}(T)$…
We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
It is well-known that an extremely accurate parametrization of the growth function of matter density perturbations in $\Lambda$CDM cosmology, with errors below $0.25 \%$, is given by $f(a)=\Omega_{m}^{\gamma} \,(a)$ with $\gamma \simeq…