scholarly journals Ideal statistical convergence and ideal statistical Cauchy sequences in two normed spaces over non archimedean fields

2020 ◽  
Author(s):  
K. Suja ◽  
S. Sangeetha
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Cauchy Sequences

scholarly journals Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar
Keyword(s):  
Statistical Convergence ◽  
Convergence Criteria ◽  
Double Sequences ◽  
Normed Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Probabilistic Normed Spaces

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

scholarly journals λ-statistical convergence in n-normed spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 141-153 ◽  
Author(s):  
Bipan Hazarika ◽  
Ekrem Savaş
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Inclusion Relations ◽  
Convergent Sequences

Abstract In this paper, we introduce the concept of λ-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and λ-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, λ)-summability in n-normed spaces

scholarly journals On statistical convergence in quasi-metric spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 225-236 ◽  
Author(s):  
Merve İlkhan ◽  
Emrah Evren Kara
Keyword(s):  
Functional Analysis ◽  
Computer Science ◽  
Distance Function ◽  
Metric Space ◽  
Statistical Convergence ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Comprehensive Investigation ◽  
Cauchy Sequences

AbstractA quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.

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 Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Saeed Sarabadan ◽  
Sorayya Talebi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences

We present various kinds of statistical convergence andℐ-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion forℐ-convergence of sequences of functions in 2-normed spaces. We also define the notion ofℐ-equistatistically convergence and studyℐ-equi-statistically convergence of sequences of functions.

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