scholarly journals Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 621-629
Author(s):  
Şükran Konca
Keyword(s):  
Statistical Convergence ◽  
Riesz Space ◽  
Double Sequences ◽  
Riesz Spaces ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
Locally Solid Riesz Space ◽  
Statistical Boundedness ◽  
Weighted Lacunary Statistical Convergence

Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.

scholarly journals Statistical Convergence of Double Sequences in Locally Solid Riesz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi ◽  
M. Mursaleen
Keyword(s):  
Statistical Convergence ◽  
Riesz Space ◽  
Double Sequences ◽  
Riesz Spaces ◽  
Locally Solid Riesz Space

Recently, the notion of statistical convergence is studied in a locally solid Riesz space by Albayrak and Pehlivan (2012). In this paper, we define and study statisticalτ-convergence, statisticalτ-Cauchy andS∗(τ)-convergence of double sequences in a locally solid Riesz space.

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 Weighted lacunary statistical convergence in locally solid Riesz spaces

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2059-2067 ◽  
Author(s):  
Metin Başarır ◽  
Şukran Konca
Keyword(s):  
Statistical Convergence ◽  
Lacunary Sequence ◽  
Riesz Spaces ◽  
Lacunary Statistical Convergence ◽  
Weighted Lacunary Statistical Convergence

In this paper we introduce the concepts of weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-bounded by combining both of the definitions of lacunary sequence and N?rlund-type mean, using a new lacunary sequence which has been defined by Basarir and Konca [3]. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces.

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.

scholarly journals Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Bipan Hazarika ◽  
Abdullah Alotaibi
Keyword(s):  
Decomposition Theorem ◽  
Riesz Space ◽  
Riesz Spaces ◽  
Inclusion Relations ◽  
Locally Solid Riesz Space ◽  
Inclusion Results ◽  
Convergent Sequences

We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of doubleθ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.

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 Ideal convergence in locally solid Riesz spaces

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 797-809 ◽  
Author(s):  
Bipan Hazarika
Keyword(s):  
Bounded Sequence ◽  
Riesz Space ◽  
Ideal Convergence ◽  
Riesz Spaces ◽  
Basic Properties ◽  
Locally Solid Riesz Space ◽  
Positive Integers ◽  
The Ideal

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal ?-convergence, ideal ?-Cauchy and ideal ?-bounded sequence in locally solid Riesz space endowed with the topology ?. Some basic properties of these concepts has been investigated. We also examine the ideal ?-continuity of a mapping defined on locally solid Riesz space.

scholarly journals On generalized statistical convergence and boundedness of Riesz space-valued sequences

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4989-5002
Author(s):  
Sudip Pal ◽  
Sagar Chakraborty
Keyword(s):  
Statistical Convergence ◽  
Necessary Conditions ◽  
Convergent Sequence ◽  
Bounded Sequence ◽  
Riesz Space ◽  
Riesz Spaces ◽  
Natural Density

We consider the notion of generalized density, namely, the natural density of weight 1 recently introduced in [4] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Also we consider similar types of results for the case of generalized statistically bounded sequence. Some results are further obtained in a more general form by using the notion of ideals. The entire investigation is performed in the setting of Riesz spaces extending the recent results in [13].

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.

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