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IMI/Publicaţii/BASM/Ediţii/BASM n.2(81), 2016/

Lacunary Ideal Convergence in Probabilistic Normed Space

Authors: Bipan Hazarika, Ayhan Esi

Abstract

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.

Bipan Hazarika
Department of Mathematics
Rajiv Gandhi University
Rono Hills, Doimukh-791112
Arunachal Pradesh, India
E-mail:

Ayhan Esi
Adiyaman University
Science and Art Faculty
Department of Mathematics
02040, Adiyaman, Turkey
E-mail:

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