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 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 Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers - doi: 10.5269/bspm.v30i2.14007

2011 ◽  
Vol 30 (2) ◽  
pp. 57-62
Author(s):  
Ayhan Esi ◽  
Necdet Çatalbas
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Lacunary Sequence ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let =(k_{r}) be a lacunary sequence. The two sequnces X  = (X_{k}) and Y=(Y_{k}) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every >0lim_{r}(1/(h_{r}))|{k∈I_{r}:d(((X_{k})/(Y_{k})),L)≥}|=0. 

scholarly journals Lacunary statistical convergence and inclusion properties between lacunary methods

2000 ◽  
Vol 23 (3) ◽  
pp. 175-180 ◽  
Author(s):  
Jinlu Li
Keyword(s):  
Statistical Convergence ◽  
Lacunary Sequence ◽  
General Description ◽  
Lacunary Sequences ◽  
Inclusion Properties ◽  
Integer Sequence ◽  
Lacunary Statistical Convergence

A lacunary sequence is an increasing integer sequenceθ={kr}such thatkr−kr−1→∞asr→∞. A sequencexis calledsθ-convergent toLprovided that for eachϵ>0,limr(1/(kr−kr−1)){the number of   kr−1<k≤kr:|xk−L|≥ϵ}=0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.

Sign in / Sign up

Export Citation Format

Share Document