Lacunary ideal convergence in probabilistic normed space

Bipan Hazarika ; Ayhan Esi

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 3-17.

Résumé

The aim of this paper is to study the notion of lacunary $I$-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary $I$-limit points and lacunary $I$-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary $I$-Cauchy sequences are introduced and studied. Finally, we provided example which shows that our method of convergence in probabilistic normed spaces is more general.

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