On the ideal convergence of sequences of Świątkowski functions

2018 ◽  
Vol 5 (1) ◽  
pp. 155-167
Author(s):  
Tomasz Natkaniec ◽  
Piotr Szuca
Keyword(s):  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
The Ideal

Weighted uniform density ideals

2018 ◽  
Vol 68 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Jacek Tryba
Keyword(s):  
Uniform Density ◽  
Topological Complexity ◽  
Ideal Convergence ◽  
Darboux Property ◽  
Analytical Properties ◽  
Banach Density ◽  
Convergence Of Sequences ◽  
The Ideal

Abstract Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of weighted uniform density ideals and consider the topological complexity of these ideals as well as when they have certain analytical properties related to the ideal convergence of sequences and series. Furthermore, we prove some inequalities between different upper and lower weighted uniform densities and give the answer to the problem concerning the Darboux property of these densities.

Ideal convergence of sequences in neutrosophic normed spaces

2021 ◽  
pp. 1-10
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
The Ideal

Statistical convergence of sequences has been studied in neutrosophic normed spaces (NNS) by Kirişci and Şimşek [39]. Ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the ideal convergence in NNS. In this paper, we study the concept of ideal convergence and ideal Cauchy for sequences in NNS.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

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 Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Saeed Sarabadan ◽  
Sorayya Talebi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences

We present various kinds of statistical convergence andℐ-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion forℐ-convergence of sequences of functions in 2-normed spaces. We also define the notion ofℐ-equistatistically convergence and studyℐ-equi-statistically convergence of sequences of functions.

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 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.

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