Rough \(\mathcal I\)-convergence
type: Item
instance of: scholarly article
title: Rough \(\mathcal I\)-convergence
zbMATH Open document ID: 1309.40002
author: Erdinç Dündar
author: Celal Çakan
published in: Demonstratio Mathematica
publication date: 2014-09-17T00:00:00Z
review text: The authors introduce the notion of rough \(\mathcal{I}\)-convergence, using the concept of \(\mathcal{I}\)-convergence and the concept of rough convergence as follows: Let \(r\) be a nonnegative real number and \(\mathcal{I}\) be a nontrivial ideal. A sequence \((x_i)\in \mathbb{R}^{n}\) is said to be rough \(\mathcal{I}\)-convergent to \(x\) if, for every \(\epsilon>0\), \[ \{i\in \mathbb{N} : \|x_i-x\|\geq r+\epsilon \}\in \mathcal{I}. \] They define the set of rough \(\mathcal{I}\)-limit points of a sequence and investigate some properties of this set.
Mathematics Subject Classification ID: 40A35
zbMATH DE Number: 6345356
zbMATH Keywords: ideal
zbMATH Keywords: rough convergence
zbMATH Keywords: \(\mathcal{I}\)-convergence
zbMATH Keywords: rough \(\mathcal{I}\)-convergence
reviewed by: Umit Totur
MaRDI profile type: Publication
full work available at URL: dema-2014-0051
OpenAlex ID: W2036483360
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DOI: 10.2478/DEMA-2014-0051
description: scientific article; zbMATH DE number 6345356