Lacunary statistically convergent double sequences in probabilistic normed spaces

2012 ◽  
Vol 58 (2) ◽  
pp. 331-339 ◽  
Author(s):  
S. A. Mohiuddine ◽  
E. Savaş
Keyword(s):  
Double Sequences ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces

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 Statistical Summability of Double Sequences through de la Vallée-Poussin Mean in Probabilistic Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Double Sequences ◽  
Normed Spaces ◽  
Summability Methods ◽  
Probabilistic Normed Spaces ◽  
De La Vallée Poussin

The purpose of this paper is to define some new types of summability methods for double sequences involving the ideas of de la Vallée-Poussin mean in the framework of probabilistic normed spaces and establish some interesting results.

scholarly journals Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
S. Karakus ◽  
K. Demırcı
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces ◽  
Single Sequence

The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilistic normed spaces. Then we display an exampl e such that our method of convergence is stronger than usual convergence on probabilistic normed spaces. Also we give a useful characterization for statistically convergent double sequences.

$\bar \lambda $-statistically convergent double sequences in probabilistic normed spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
E. Savaş ◽  
S. Mohiuddine
Keyword(s):  
Normed Space ◽  
Double Sequences ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Probabilistic Normed Spaces ◽  
Cauchy Sequences

AbstractThe purpose of this paper is to introduce and study the concepts of double $\bar \lambda $-statistically convergent and double $\bar \lambda $-statistically Cauchy sequences in probabilistic normed space.

scholarly journals On ideal convergence of double sequences in probabilistic normed spaces

2012 ◽  
Vol 28 (8) ◽  
pp. 1689-1700 ◽  
Author(s):  
Vijay Kumar ◽  
Bernardo Lafuerza-Guillén
Keyword(s):  
Double Sequences ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Probabilistic Normed Spaces

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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