Rough weighted statistical convergence on locally solid Riesz spaces

Positivity ◽  
2021 ◽  
Author(s):  
Sanjoy Ghosal ◽  
Mandobi Banerjee
Keyword(s):  
Statistical Convergence ◽  
Riesz Spaces

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 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 Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Xuemei Xue ◽  
Jian Tao
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Banach Lattices ◽  
Order Convergence ◽  
Riesz Spaces ◽  
Monotone Sequences ◽  
Cauchy Sequences ◽  
Relatively Uniform Convergence

A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.

On Iλ-Statistical Convergence in Locally Solid Riesz Spaces

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Pratulananda Das ◽  
Ekrem Savas
Keyword(s):  
Statistical Convergence ◽  
General Idea ◽  
Riesz Spaces

AbstractIn this paper, we extend some results concerning statistical convergence in locally solid Riesz spaces by introducing a more general idea of convergence, namely I

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.

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