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ЖУРНАЛЫ // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Архив

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, номер 2, страницы 3–17 (Mi basm420)

Lacunary ideal convergence in probabilistic normed space

Bipan Hazarikaa, Ayhan Esib

a Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India
b Adiyaman University, Science and Art Faculty, Department of Mathematics, 02040, Adiyaman, Turkey

Аннотация: 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.

Ключевые слова и фразы: ideal convergence, probabilistic normed space, lacunary sequence, $\theta$-convergence.

MSC: 40G15, 46S70, 54E70

Поступила в редакцию: 04.11.2013

Язык публикации: английский



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