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A Short and Partial History of Probabilistic Normed Spaces

Mediterranean Journal of Mathematics, 2006
This contribution aims at presenting a survey of a portion of the theory of Probabilistic Normed spaces. No result will be proved, so that the reader is referred to the original sources for the proofs. The theory of PN spaces has many facets and touches on many branches of mathematics, for instance, geometry, functional analysis, topology, probability.
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Compact Linear Operators Between Probabilistic Normed Spaces

2008
A pair (X, N) is said to be a probabilistic normed space if X is a real vector space, N is a mapping from X into the set of all distribution functions (for x ∈ X, the distribution function N(x) is denoted by N x , and N x (t) is the value N x at t ∈ ℝ) satisfying the following conditions: (N1) N x (0) = 0 (N2) N x (t) = 1 for all t >
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I-statistical convergence in probabilistic normed spaces

2020
In this paper, we introduce a new type of summability notion, namely, I - statistical convergence and I -lacunary statistical convergence for double sequences in probabilistic normed space, which is a natural generalization of the notion of natural density, statistical convergence and lacunary statistical convergence using the notion of ideals of the ...
GÜRDAL, Mehmet, Savas, Ekrem
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On Compactness in Probabilistic Normed Spaces

2020
Fatkić, Berina, Fatkić, Jasmina
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On the Completeness in Probabilistic Normed Spaces

2020
Fatkić, Berina   +2 more
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