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StatisticallyD-bounded sequences in probabilistic normed spaces
Applicable Analysis, 2009In this study, the concept of a statistically D-bounded sequence in a probabilistic normed (PN) space endowed with the strong topology is introduced and its basic properties are investigated. It is shown that a strongly statistically convergent sequence and a strong statistically Cauchy sequence are statistically D-bounded under certain conditions.
Sencimen, C., Pehlivan, S.
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Probabilistic norm of linear operators on PN space
Applied Mathematics and Mechanics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao, Jianzhong, Jiang, Xingguo
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A NEW APPROACH FOR PROBABILISTICALLY BOUNDED SETS IN MENGER PROBABILISTIC NORMED SPACES
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008The main purpose of this paper is to introduce a new topological structure which is called fuzzifying topological structure determined by the method of co-tower topologies in Menger probabilistic normed spaces. We prove that the fuzzifying topological structure is compatible with the vector structure.
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A Short and Partial History of Probabilistic Normed Spaces
Mediterranean Journal of Mathematics, 2006This 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
2008A 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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On the definition of a probabilistic normed space
, 1992C. Alsina +8 more
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I-statistical convergence in probabilistic normed spaces
2020In 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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A New Type of Ideal Convergence of Difference Sequence in Probabilistic Normed Space
, 2018V. Khan +2 more
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ON UNIFORM CONVERGENCE OF LINEAR OPERATORS ON THE PROBABILISTIC NORMED SPACE
, 1989张石生, 李向荣, 陈志坚
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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