Generalized Statistical Convergence for Sequences of Function in Random 2-Normed Spaces

2018 ◽  
pp. 296-308
Author(s):  
Ekrem Savaş ◽  
Mehmet Gürdal
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Sequences Of Function

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 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 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.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

Sign in / Sign up

Export Citation Format

Share Document