Strong almost convergence and almost λ-statistical convergence

Advances in Almost Convergence

In this paper, we first give the concept of properly distributed sequence, and prove that it is almost convergent with F-limit expressed as a formal integral. Basing on these, we review the work of Feng and Li, which is shown to be a special case of our generalized theory. Then we generalize Banach limit to Banach limit functional, which is the minimum requirement to characterize strong almost ...

Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms

We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi-Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the rst result on almost everywhere strong convergence in dimension greater than two.

Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a ...

Almost sure convergence, convergence in probability and asymptotic normality

In the previous chapter we considered estimator of several different parameters. The hope is that as the sample size increases the estimator should get ‘closer’ to the parameter of interest. When we say closer we mean to converge. In the classical sense the sequence {xk} converges to x (xk → x), if |xk − x| → 0 as k → ∞ (or for every ε > 0, there exists an n where for all k > n, |xk − x| < ε). ...