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.

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 Rough I2-Lacunary Statistical Convergence of Double Sequences

2018 ◽  
Author(s):  
Ömer Kişi ◽  
Erdinç Dündar
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Limit Set ◽  
Double Sequences ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence

In this paper, we introduce and study the notion of rough I2-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I2-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

scholarly journals On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Cemal Belen ◽  
Mustafa Yildirim
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Double Sequence Spaces ◽  
Lacunary Statistical Convergence

AbstractIn this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods

scholarly journals Lacunary statistical convergence of double sequences of sets

2015 ◽  
Vol 20 (7) ◽  
pp. 2883-2888 ◽  
Author(s):  
Fatih Nuray ◽  
Uğur Ulusu ◽  
Erdinç Dündar
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Lacunary Statistical Convergence

scholarly journals Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

2018 ◽  
Vol 36 (1) ◽  
pp. 161 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Sliding Window ◽  
Modulus Function ◽  
Convergence Criterion ◽  
Sequential Methods ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence

In this paper we study the concepts of sliding window convergence for real valued measurable functions dened on [0,1) via modulus function. We also establish some inclusions and consistency theorems for sequential methods along with examples. Finally, we give a Cauchy convergence criterion.

scholarly journals f-LACUNARY STATISTICAL CONVERGENCE AND STRONG f-LACUNARY SUMMABILITY OF ORDER α OF DOUBLE SEQUENCES

2020 ◽  
pp. 495
Author(s):  
Hacer Sengul ◽  
Mikail Et ◽  
Yavuz Altın
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations

The main object of this article is to introduce the concepts of f-lacunary statistical convergence of order alpha and strong f-lacunary summability of order alpha of double sequences and give some inclusion relations between these concepts.

scholarly journals Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Double Sequence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Lacunary Statistical Convergence ◽  
Cesaro Convergence

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

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