Abstract. In this paper, we present some relationships between convergence and uniform statistical convergence of a given sequence and its subsequences. The results concerning uniform statistical convergence presented here are also closely related to earlier results regarding statistical convergence and almost convergence of sequences, and are dealing with measure and in a minor case with category. Finally, we present a Cauchy type characterization of uniform statistical convergence and a result concerning uniform statistical convergence of subseries of a series.
We study the concepts of I-limit and I-cluster points of a sequence, where I is an ideal with the Baire property. We obtain the relationship between I-limit and I-cluster points of a subsequence of a given sequence and the set of its classical limit points in the sense of category theory.
In this paper, we present some results linking the uniform statistical limit superior and inferior, almost convergence and uniform statistical convergence of a sequence. We also study the relationship between the set of uniform statistical cluster points of a given sequence and its subsequences. The results concerning uniform statistical convergence and uniform statistical cluster points presented here are also closely related to earlier results regarding statistical convergence and statistical cluster points of a sequence.
The sequence x = (x k ) is quasi-statistically convergent to L provided that for each " > 0, lim n 1 cn jfk n : jx k Lj "gj = 0 where lim n cn = 0; cn > 0 for each n 2 N and lim sup n cn n < 1: In this paper quasi-statistical convergence is compared with statistical convergence and other methods. Furthermore a decomposition theorem is proved and a factorization result is also given for quasi-statistical convergence.
scite is a Brooklyn-based startup that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.