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 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 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 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 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 some double almost lacunary sequence spaces defined by Orlicz functions

Filomat ◽  
2005 ◽  
pp. 35-44 ◽  
Author(s):  
Ekrem Savas ◽  
Richard Patterson
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Orlicz Functions ◽  
Lacunary Statistical Convergence

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

On certain spaces of double sequences by de la Vallée-Poussin mean

2015 ◽  
Vol 08 (04) ◽  
pp. 1550079 ◽  
Author(s):  
Kuldip Raj ◽  
Suruchi Pandoh
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Difference ◽  
Double Sequences ◽  
Normed Spaces ◽  
Interval Numbers ◽  
Convergence Spaces ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
De La Vallée Poussin

In this paper, we introduce some [Formula: see text]-convergence spaces of double difference sequences of interval numbers with Musielak–Orlicz function [Formula: see text] over [Formula: see text]-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. Furthermore, we study [Formula: see text]-statistical convergence of double difference sequences of interval numbers.

scholarly journals Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Ugur Kadak
Keyword(s):  
Fractional Order ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Fixed Sequence ◽  
Related Sequence ◽  
Lacunary Sequences ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
The Relationship ◽  
Difference Sequence Spaces

We generalize the lacunary statistical convergence by introducing the generalized difference operatorΔναof fractional order, whereαis a proper fraction andν=(νk)is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.

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.

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