On ideal convergence in probabilistic normed spaces

Rok, strany: 2012, 49 - 62

An interesting generalization of statistical convergence is $I$-convergence which was introduced by P. Kostyrko et al [KOSTYRKO, P.---ŠALÁT, T.---WILCZYŃSKI, W.: \textit{$\mathcal{I}$-Convergence}, Real Anal. Exchange \textbf{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.

ISO 690:

Mursaleen, M., Mohiuddine, S. 2012. On ideal convergence in probabilistic normed spaces. In Mathematica Slovaca, vol. 62, no.1, pp. 49-62. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0071-9

APA:

Mursaleen, M., Mohiuddine, S. (2012). On ideal convergence in probabilistic normed spaces. Mathematica Slovaca, 62(1), 49-62. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0071-9