Weak statistical convergence and weak filter convergence for unbounded sequences

On Weak Statistical Convergence

The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

Weak Convergence and Weak* Convergence1

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By...

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 ...

Research Article On Weak Statistical Convergence

Weak convergence of the tail empirical process for dependent sequences

This paper proves weak convergence in D of the tail empirical process – the renormalized extreme tail of the empirical process – for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covari...