scholarly journals Statistical convergence through de la Vallée-Poussin mean in locally solid Riesz spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Syed Abdul Mohiuddine ◽  
Abdullah Alotaibi ◽  
Mohammad Mursaleen
Keyword(s):  
Statistical Convergence ◽  
Riesz Spaces ◽  
De La Vallée Poussin

scholarly journals Statistical Summability through de la Vallée-Poussin Mean in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ayhan Esi
Keyword(s):  
Statistical Convergence ◽  
The Other ◽  
Normed Spaces ◽  
Summability Methods ◽  
Probabilistic Normed Spaces ◽  
New Type ◽  
De La Vallée Poussin

Two concepts—one of statistical convergence and the other of de la Vallée-Poussin mean—play an important role in recent research on summability theory. In this work we define a new type of summability methods and statistical completeness involving the ideas of de la Vallée-Poussin mean and statistical convergence in the framework of probabilistic normed 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.

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 Statistical Tauberian theorems for Cesàro integrability mean based on post-quantum calculus

2020 ◽  
Vol 9 (3) ◽  
pp. 653-663
Author(s):  
P. Parida ◽  
S. K. Paikray ◽  
B. B. Jena
Keyword(s):  
Continuous Function ◽  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Quantum Calculus ◽  
Cesaro Summability ◽  
Single Integral ◽  
De La Vallée Poussin

Abstract The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

scholarly journals Some Tauberian conditions on logarithmic density

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Adem Kılıçman ◽  
Stuti Borgohain ◽  
Mehmet Küçükaslan
Keyword(s):  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Logarithmic Density ◽  
Tauberian Conditions ◽  
De La Vallée Poussin

Abstract This article is based on the study on the λ-statistical convergence with respect to the logarithmic density and de la Vallee Poussin mean and generalizes some results of logarithmic λ-statistical convergence and logarithmic $(V,\lambda )$ ( V , λ ) -summability theorems. Hardy’s and Landau’s Tauberian theorems to the statistical convergence, which was introduced by Fast long back in 1951, have been extended by J.A. Fridy and M.K. Khan (Proc. Am. Math. Soc. 128:2347–2355, 2000) in recent years. In this article we try to generalize some Tauberian conditions on logarithmic statistical convergence and logarithmic $(V,\lambda )$ ( V , λ ) -statistical convergence, and we find some new results on it.

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