A metric for weak convergence of distribution functions

Weak Convergence of Random Functions

Let {vij}, i, j = 1, 2, . . . , be i.i.d. symmetric random variables with E(v 11) < ∞, and for each n let Mn = 1 sVnV T n , where Vn = (vij), i = 1, 2, . . . , n, j = 1, 2, . . . , s = s(n), and n/s → y > 0 as n → ∞. Denote by OnΛnO n the spectral decomposition of Mn. Define X ∈ D[0, 1] by Xn(t) = √ n 2 ∑[nt] i=1(y 2 i − 1 n), where (y1, y2, . . . , yn) = O (± 1 √ n ,± 1 √ n , . . . ,± 1 √ n ) ...

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

On Weak Convergence of Locally Periodic Functions

We have not found proofs of these facts in the literature. The aim of this paper is to present such proofs. Moreover, we show that the first statement also holds for the case p = 1. The two facts described above are used in the proof of the reiterated homogenization result for monotone operators, see [14] and [15]. The solution uξh is used to define a sequence of functions similar to the ones i...

Weak and strong convergence theorems for a finite family of generalized asymptotically quasinonexpansive nonself-mappings

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

The Weak Convergence for Functions of Negatively Associated Random Variables