On ideal convergence in probabilistic normed spaces |
| |
Authors: | M Mursaleen S A Mohiuddine |
| |
Institution: | 1.Department of Mathematics,Aligarh Muslim University,Aligarh,India;2.Department of Mathematics Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|