On ideal convergence in probabilistic normed spaces

An interesting generalization of statistical convergence is I -convergence which was introduced by P.Kostyrko et al [KOSTYRKO,P.—ŠALÁT,T.—WILCZYŃSKI,W.: I-Convergence , Real Anal. Exchange 26 (2000–2001), 669–686]. In this paper, we define and study the concept of I -convergence, I *-convergence, I...

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Bibliographic Details
Published in:Mathematica Slovaca Vol. 62; no. 1; pp. 49 - 62
Main Authors: Mursaleen, M., Mohiuddine, S. A.
Format: Journal Article
Language:English
Published: Heidelberg SP Versita 01.02.2012
Versita
Subjects:
Algebra
I-cluster points
I-convergence
I-limit points
Mathematics
Mathematics and Statistics
Primary 40A05
probabilistic normed space
Secondary 46A70
t-norm
cluster points
convergence
Primary 40A05
limit points
t-norm
probabilistic normed space
Secondary 46A70
ISSN:0139-9918, 1337-2211
Online Access:Get full text
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Summary:An interesting generalization of statistical convergence is I -convergence which was introduced by P.Kostyrko et al [KOSTYRKO,P.—ŠALÁT,T.—WILCZYŃSKI,W.: I-Convergence , Real Anal. Exchange 26 (2000–2001), 669–686]. In this paper, we define and study the concept of I -convergence, I *-convergence, I -limit points and I -cluster points in probabilistic normed space. We discuss the relationship between I -convergence and I *-convergence, i.e. we show that I *-convergence implies the I -convergence in probabilistic normed space. Furthermore, we have also demonstrated through an example that, in general, I -convergence does not imply I *-convergence in probabilistic normed space.
ISSN:0139-9918
1337-2211
DOI:10.2478/s12175-011-0071-9