scholarly journals On the relationship between ideal cluster points and ideal limit points

2019 ◽  
Vol 252 ◽  
pp. 178-190 ◽  
Author(s):  
Marek Balcerzak ◽  
Paolo Leonetti
Keyword(s):  
Limit Points ◽  
The Relationship ◽  
Cluster Points ◽  
Ideal Limit

scholarly journals Category theoretical view of I-cluster and I-limit points of subsequences

2020 ◽  
Vol 24 (1) ◽  
pp. 103-108
Author(s):  
Leila Miller-Van Wieren ◽  
Emre Taş ◽  
‪Tuğba Yurdakadim
Keyword(s):  
Category Theory ◽  
Classical Limit ◽  
Baire Property ◽  
Theoretical View ◽  
Limit Points ◽  
The Relationship ◽  
Cluster Points

We study the concepts of I-limit and I-cluster points of a sequence, where I is an ideal with the Baire property. We obtain the relationship between I-limit and I-cluster points of a subsequence of a given sequence and the set of its classical limit points in the sense of category theory.

scholarly journals New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ö. Kişi ◽  
M. B. Huban ◽  
M. Gürdal
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Double Sequence ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Number Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
The Relationship ◽  
Cluster Points

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

2021 ◽  
Vol 10 (9) ◽  
pp. 3175-3184
Author(s):  
Leila Miller-Van Wieren
Keyword(s):  
Real Numbers ◽  
Statistical Cluster ◽  
Different Types ◽  
Limit Points ◽  
Cluster Points

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

scholarly journals On subsequential limit points of a sequence of iterates. II

1985 ◽  
Vol 38 (1) ◽  
pp. 118-129
Author(s):  
M. Maiti ◽  
A. C. Babu
Keyword(s):  
Continuous Function ◽  
Distance Function ◽  
Metric Space ◽  
Product Space ◽  
Topological Spaces ◽  
Limit Points ◽  
Cluster Points

AbstractJ. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.

scholarly journals On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Normed Space ◽  
Complex Numbers ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Positive Integers ◽  
Cluster Points

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

scholarly journals On rough convergence in 2-normed spaces and some properties

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5077-5086
Author(s):  
Mukaddes Arslan ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Fixed Sequence ◽  
Limit Points ◽  
Cluster Points

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

scholarly journals Wijsman Rough λ Statistical Convergence of Order α of Triple Sequence of Functions

2017 ◽  
Vol 2 (1) ◽  
pp. 07-15
Author(s):  
A. Esi ◽  
N. Subramanian ◽  
M. Aiyub
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Natural Density ◽  
Limit Points ◽  
Cluster Points ◽  
Sequence Of Functions

In this paper, using the concept of natural density, we introduce the notion of Wijsman rough λ statistical convergence of order α triple sequence of functions. We define the set of Wijsman rough λ statistical convergence of order α of limit points of a triple sequence spaces of functions and obtain Wijsman λ statistical convergence of order α criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Wijsman rough λ statistical convergence of order α of cluster points and the set of Wijsman rough λ statistical convergence of order α limit points of a triple sequences of functions.

scholarly journals Lacunary Statistical Limit Points in Random 2-Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
A. Güncan ◽  
U. Yamancı ◽  
M. Gürdal
Keyword(s):  
Normed Spaces ◽  
Statistical Limit ◽  
Limit Points ◽  
Cluster Points

We introduce the notion θ-cluster points, investigate the relation between θ-cluster points and limit points of sequences in the topology induced by random 2-normed spaces, and prove some important results.

Sign in / Sign up

Export Citation Format

Share Document