2014/05/14 by Bipan Hazarika, Hazarika, Bipan, Ayhan Eşi +2
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Mathematical Approximation and Integration #math.FA #msc:40G15 #msc:46S70 #msc:54E70
paper · pdf · doi:10.48550/arxiv.1405.3619
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arxiv created 2014/05/14 · arxiv updated 2014/05/15
An ideal I is a family of subsets of positive integers ℕ which is closed under taking finite unions and subsets of its elements. A sequence (xk) of real numbers is said to be lacunary I-convergent to a real number ℓ, if for each ε> 0 the set \r∈ ℕ:(1)/(hr)∑k∈ Jr |xk-ℓ|≥ ε\ belongs to I. 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.