Some spaces of weighted lacunary B^m_eta-convergent sequences defined by an Orlicz function and B^m_eta-weighted lacunary statistical convergence

2012 ◽  
Vol 2 (2) ◽  
Author(s):  
Metin Başarır ◽  
Şükran Konca
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Lacunary Statistical Convergence ◽  
Weighted Lacunary Statistical Convergence ◽  
Convergent Sequences

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.

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.

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 Density by Moduli and Lacunary Statistical Convergence

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Vinod K. Bhardwaj ◽  
Shweta Dhawan
Keyword(s):  
Strong Convergence ◽  
Tauberian Theorem ◽  
Statistical Convergence ◽  
General Description ◽  
Lacunary Statistical Convergence ◽  
Bounded Sequences ◽  
Convergent Sequences

We have introduced and studied a new concept off-lacunary statistical convergence, wherefis an unbounded modulus. It is shown that, under certain conditions on a modulusf, the concepts of lacunary strong convergence with respect to a modulusfandf-lacunary statistical convergence are equivalent on bounded sequences. We further characterize thoseθfor whichSθf=Sf, whereSθfandSfdenote the sets of allf-lacunary statistically convergent sequences andf-statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods off-statistical convergence is given. Finally, we give anSθf-analog of the Cauchy criterion for convergence and a Tauberian theorem forSθf-convergence is also proved.

Lacunary statistical convergence of order (α, β) in topological groups

2017 ◽  
Vol 26 (3) ◽  
pp. 339-344
Author(s):  
HACER SENGUL ◽  
◽  
MIKAIL ET ◽  
Keyword(s):  
Statistical Convergence ◽  
Topological Groups ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
Convergent Sequences

In this paper, the concept of lacunary statistical convergence of order (α, β) is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order (α, β) and the set of all lacunary statistically convergent sequences of order (α, β) are given.

scholarly journals Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Sunil K. Sharma ◽  
Dina A. Abuzaid
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Normed Spaces ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We first define the notion of lacunary statistical convergence of order (α,β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M=(Mk) of order (α,β). We also examine some topological properties and prove inclusion relations between the resulting sequence spaces.

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