On the ideal convergence of sequences of quasi-continuous functions

2015 ◽  
pp. 1-12
Author(s):  
Tomasz Natkaniec ◽  
Piotr Szuca
Keyword(s):  
Continuous Functions ◽  
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 Near-rings of continuous functions on disconnected groups

1979 ◽  
Vol 28 (4) ◽  
pp. 433-451 ◽  
Author(s):  
Robert D. Hofer
Keyword(s):  
Topological Group ◽  
Identity Element ◽  
Continuous Functions ◽  
Ideal Structure ◽  
Rings Of Continuous Functions ◽  
The Ideal

AbstractN(G) denotes the near-ring of all continuous selfmaps of the topological group G (under composition and the pointwise induced operation) and N0(G) is the subnear-ring of N(G) consisting of all functions having the identity element of G fixed. It is known that if G is discrete then (a) N0(G) is simple and (b) N(G) is simple if and only if G is not of order 2. We begin a study of the ideal structure of these near-rings when G is a disconnected group.

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.

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