On ideal convergence in probabilistic normed spaces - Mursaleen, M.; Mohiuddine, S. A. (Mathematica Slovaca, 2012)
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.