scholarly journals On the Ideal Convergence of Double Sequences in Locally Solid Riesz Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. Alotaibi ◽  
B. Hazarika ◽  
S. A. Mohiuddine
Keyword(s):  
Double Sequences ◽  
Ideal Convergence ◽  
Riesz Spaces ◽  
The Ideal

The aim of this paper is to define the notions of ideal convergence,I-bounded for double sequences in setting of locally solid Riesz spaces and study some results related to these notions. We also define the notion ofI*-convergence for double sequences in locally solid Riesz spaces and establish its relationship with ideal convergence.

scholarly journals Ideal convergence in locally solid Riesz spaces

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 797-809 ◽  
Author(s):  
Bipan Hazarika
Keyword(s):  
Bounded Sequence ◽  
Riesz Space ◽  
Ideal Convergence ◽  
Riesz Spaces ◽  
Basic Properties ◽  
Locally Solid Riesz Space ◽  
Positive Integers ◽  
The Ideal

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal ?-convergence, ideal ?-Cauchy and ideal ?-bounded sequence in locally solid Riesz space endowed with the topology ?. Some basic properties of these concepts has been investigated. We also examine the ideal ?-continuity of a mapping defined on locally solid Riesz space.

scholarly journals IDEAL CONVERGENCE OF DOUBLE SEQUENCES OF CLOSED SETS

2021 ◽  
pp. 605
Author(s):  
Ozer Talo ◽  
Yurdal Sever
Keyword(s):  
Metric Space ◽  
Double Sequence ◽  
Double Sequences ◽  
Ideal Convergence ◽  
Closed Sets ◽  
The Ideal

In the present paper, we introduce the concepts of ideal inner and ideal outer limits which always exist even if empty sets for double sequences of closed sets in Pringsheim's sense. Next, we give some formulas for finding ideal inner and outer limits in a metric space. After then, we define Kuratowski ideal convergence of double sequences of closed sets by means of the ideal inner and ideal outer limits of a double sequence of closed sets. Additionally, we give some examples that our result is more general than the results obtained before.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals Mad families, P+(I)-ideals and ideal convergence

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3099-3108
Author(s):  
Jiakui Yu ◽  
Shuguo Zhang
Keyword(s):  
Necessary Condition ◽  
Ideal Convergence ◽  
Mad Families ◽  
Helly Property ◽  
Almost Disjoint ◽  
Almost Disjoint Families ◽  
The Ideal

Let I be an ideal on ?, the notion of I-AD family was introduced in [3]. Analogous to the well studied ideal I(A) generated by almost disjoint families, we introduce and investigate the ideal I(I-A). It turns out that some properties of I(I-A) depends on the structure of I. Denoting by a(I) the minimum of the cardinalities of infinite I-MAD families, several characterizations for a(I) ? ?1 will be presented. Motivated by the work in [23], we introduce the cardinality s?,?(I), and obtain a necessary condition for s?,?(I) = s(I). As an application, we show finally that if a(I) ? s(I), then BW property coincides with Helly property.

Wijsman regularly ideal convergence of double sequences of sets

2019 ◽  
Vol 37 (6) ◽  
pp. 8159-8166 ◽  
Author(s):  
Erdinç Dündar ◽  
Nimet Pancaroğlu Akın
Keyword(s):  
Double Sequences ◽  
Ideal Convergence

scholarly journals Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Awad A. Bakery ◽  
Elsayed Abdelbayen Elnour Mohamed ◽  
Mohamed Alamin Ahmed
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relation ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
De La Vallée Poussin ◽  
Difference Sequence Spaces ◽  
The Ideal

In the present paper we introduced the ideal convergence of generalized difference sequence spaces combining de La Vallée-Poussin mean and Musielak-Orlicz function overn-normed spaces. We also study some topological properties and inclusion relation between these spaces.

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