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.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

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.

scholarly journals Lacunary Statistical Convergence of Sequences of Real-Valued Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
A. Gökhan
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences

We introduce the concepts of the lacunary statistical convergence of sequences of real-valued functions. We also give the relation between this convergence and strongly lacunary and pointwise statistical convergence. Furthermore we introduce the concept of a lacunary statistical Cauchy sequence for functional sequences and prove that it is equivalent to lacunary statistical convergence of sequences of real-valued functions.

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.

On Wijsman ℐ2-Lacunary Statistical Convergence for Double Set Sequences

2016 ◽  
Vol 57 (1) ◽  
pp. 91-104
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
The Relationship

AbstractThe aim of present work is to present some inclusion relations between the concepts of Wijsman ℐ2–lacunary statistical convergence and Wijsman strongly ℐ2–lacunary convergence for double sequences of sets. Also we study the concepts of Wijsman ℐ2–statistical convergence, Wijsman ℐ2– lacunary statistical convergence double sequences of sets and investigate the relationship among them.

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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