Statistical order convergence and statistically relatively uniform convergence in Riesz spaces
type: Item
instance of: scholarly article
title: Statistical order convergence and statistically relatively uniform convergence in Riesz spaces
zbMATH Open document ID: 1400.40004
DOI: 10.1155/2018/9092136
author: Xuemei Xue
author: Jian Tao
published in: Journal of Function Spaces
publication date: 2018-05-15T00:00:00Z
review text: Summary: A new concept of statistically \(e\)-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically \(e\)-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.
Mathematics Subject Classification ID: 40J05
Mathematics Subject Classification ID: 40A35
zbMATH DE Number: 6868715
zbMATH Keywords: Riesz spaces
zbMATH Keywords: statistical order convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9092136
OpenAlex ID: W2802059610
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description: scientific article; zbMATH DE number 6868715