scholarly journals On Kuratowski I-convergence of sequences of closed sets

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 899-912
Author(s):  
Özer Talo ◽  
Yurdal Sever
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
Positive Integers ◽  
The Relationship ◽  
Convergent Sequences

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Ba?ar) to I-inner and I-outer limits and give some I-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I-convergence for a sequence of closed sets and get some properties for Kuratowski I-convergent sequences. Also, we examine the relationship between Kuratowski I-convergence and Hausdorff I-convergence.

On statistical convergence of sequences of closed sets in metric spaces

2021 ◽  
Vol 71 (2) ◽  
pp. 409-422
Author(s):  
Dimitrios Georgiou ◽  
Athanasios Megaritis ◽  
Georgios Prinos ◽  
Fotini Sereti
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
The Relationship

Abstract In this paper, we do further investigations on the statistical inner and outer limits of sequences of closed sets in metric spaces, which were introduced by Nuray, Rhoades, and Talo, Sever, Başar, and generalize the conventional Painleve-Kuratowski inner and outer limits. Also, we provide criteria for checking statistical Wijsman and Hausdorff set convergences and we examine the relationship between Kuratowski and Wijsman statistical convergence. A closer look on the concept of statistical Cauchyness, with respect to the Hausdorff “extended” metric h, completes this research.

scholarly journals On statistically convergent sequences of closed sets

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1497-1509 ◽  
Author(s):  
Özer Talo ◽  
Yurdal Sever ◽  
Feyzi Başarc
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
The Relationship ◽  
Convergent Sequences

In this paper, we give the definitions of statistical inner and outer limits for sequences of closed sets in metric spaces. We investigate some properties of statistical inner and outer limits. For sequences of closed sets if its statistical outer and statistical inner limits coincide, we say that the sequence is Kuratowski statistically convergent. We prove some proporties for Kuratowski statistically convergent sequences. Also, we examine the relationship between Kuratowski statistical convergence and Hausdorff statistical convergence.

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

scholarly journals I-lacunary statistical convergence of sequences of sets

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1567-1574 ◽  
Author(s):  
Uğur Ulusu ◽  
Erdinç Dündar
Keyword(s):  
Statistical Convergence ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
The Relationship

In this paper we study the concepts of Wijsman I-statistical convergence, Wijsman I-lacunary statistical convergence and Wijsman strongly I-lacunary convergence of sequences of sets and investigate the relationship between them.

sp− Closedness and sp − Convergent Sequences in Intuitionistic Fuzzy Metric Space

2021 ◽  
Author(s):  
vakeel A. khan ◽  
MOBEEN AHMAD ◽  
Izhar Ali khan
Keyword(s):  
Present Article ◽  
Metric Space ◽  
Metric Spaces ◽  
Convergent Sequence ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Closed Sets ◽  
Intuitionistic Fuzzy ◽  
Convergent Sequences

Abstract The aim of present article is to introduce the concepts of sp– convergent sequence in intuitionistic fuzzy metric spaces and analyze relations of convergence, sp– convergence, s∞– convergence and st– convergence in intuitionistic fuzzy metric spaces. Further, we examine sp– convergence, s∞– convergence and st– convergence using the subsequence of convergent sequence in intuitionistic fuzzy metric spaces. Stationary intuitionistic fuzzy metric spaces are defined and investigated. We Finally define sp– closed sets, s∞– closed sets and st– closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.

scholarly journals I-divergence and I∗-divergence in cone metric spaces

2019 ◽  
Vol 13 (08) ◽  
pp. 2050139
Author(s):  
Amar Kumar Banerjee ◽  
Anirban Paul
Keyword(s):  
Normed Space ◽  
Metric Spaces ◽  
Decomposition Theorem ◽  
Cone Metric Spaces ◽  
The Relationship ◽  
Cone Metric ◽  
Convergent Sequences

In this paper, we have studied the ideas of [Formula: see text]-divergence and [Formula: see text]-divergence of sequences in cone metric spaces. We have investigated the relationship between [Formula: see text]-divergence and [Formula: see text]-divergence and their equivalence under certain condition. Further, we prove a decomposition theorem for [Formula: see text]-convergent sequences in a cone normed space.

On statistical convergence in fuzzy metric spaces

2020 ◽  
Vol 39 (3) ◽  
pp. 3987-3993
Author(s):  
Changqing Li ◽  
Yanlan Zhang ◽  
Jing Zhang
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Active Area ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Cauchy Sequences ◽  
Convergent Sequences

The idea of statistical convergence, which was first introduced by Fast and Steinhaus independently in 1951, has become one of the most active area of research in the field of mathematics. Recently, it has been applied to the realm of metrics by several authors and some useful results have been obtained. However, the existence of non-completable fuzzy metric spaces, in the sense of George and Veeramani, demonstrates that the theory of fuzzy metrics seem to be richer than that of metrics. In view of this, we attempt to generalize this convergence to the realm of fuzzy metrics. Firstly, we introduce the concept of sts-convergence in fuzzy metric spaces. Then we characterize those fuzzy metric spaces in which all convergent sequences are sts-convergent. Finally, we study sts-Cauchy sequences in fuzzy metric spaces and sts-completeness of fuzzy metric spaces.

scholarly journals On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δnm-statistical convergence

2012 ◽  
Vol 20 (1) ◽  
pp. 417-430 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Hemen Dutta
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Orlicz Functions ◽  
The Relationship ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

Abstract In this article, we introduce the lacunary difference sequence spaces w0(M, θ, Δnm, p, q), w1(M, θ, Δnm, p, q) and w∞(M, θ, Δnm, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of q-lacunary Δnm-statistical convergent sequences. Further, we study the relationship between q-lacunary n m-statistical convergent sequences and Δnm the spaces w0(M, θ, Δnm, p, q) and w1(M, θ, Δnm, p, q).

The Arzelà–Ascoli theorem by means of ideal convergence

2018 ◽  
Vol 25 (3) ◽  
pp. 475-479
Author(s):  
Emre Taş ◽  
Tugba Yurdakadim
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
The Relationship

AbstractIn this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà–Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.

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