On ideal convergence in probabilistic normed spaces

By Mohammad Mursaleen, Syed Abdul Mohiuddine. 2012

153 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/461afd405d6dbc74f3f4643f1b9bdc5d0b6109db

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Aiyub
2. Bipan Hazarika
3. Syed Abdul Mohiuddine

In Numerical Analysis

1. Bipan Hazarika
2. Ahmad M. Alghamdi
3. M. Aiyub
4. Syed Abdul Mohiuddine

In Statistics and Probability

1. M. Aiyub
2. Bipan Hazarika
3. Ahmad M. Alghamdi
4. Syed Abdul Mohiuddine
5. B. Tripathy

Citations in the corpus

• Lacunary statistical convergence in random 2-normed spaces (2012, background): “in probabilistic normed space [9,14,20, 21,24]; in intuitionistic fuzzy normed spaces [12,16,17, 19]; and in fuzzy/random 2-normed space [13,22].”
• Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems (2019, background): “It was further investigated by many authors, e.g. S̆alát et al. [43], Mursaleen and Mohiuddine [39], Hazarika and Mohiuddine [35] and references therein.”