Results 261 to 270 of about 4,634,933 (288)
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2001
In 1942 K. Menger introduced the notion of a statistical metric space as a natural generalization of the notion of a metric space (M, d) in which the distance d(p, q) (p, q ∈ M) between p and q is replaced by a distribution function F p, q ∈ Δ+. F p,q (x) can be interpreted as the probability that the distance between p and q is less than x.
Olga Hadžić, Endre Pap
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In 1942 K. Menger introduced the notion of a statistical metric space as a natural generalization of the notion of a metric space (M, d) in which the distance d(p, q) (p, q ∈ M) between p and q is replaced by a distribution function F p, q ∈ Δ+. F p,q (x) can be interpreted as the probability that the distance between p and q is less than x.
Olga Hadžić, Endre Pap
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Probabilistic b-Metric Spaces and Nonlinear Contractions [PDF]
Fixed Point Theory and Applications, 2017 AbstractThis work is for giving the probabilistic aspect to the knownb-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.
Abderrahim Mbarki
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2003
This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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Complete probabilistic metric spaces
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1971Menger [4] initiated the study of probabilistic metric spaces in 1942. A probabilistic metric space (briefly a PM space) is a space in which the "distance" between any two points is a probability distribution function. These spaces are assumed to satisfy axioms which are quite similar to the axioms satisfied in an ordinary metric space.
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Probabilistic enhancement of approximate indexing in metric spaces
Information Systems, 2013Abstract Some approximate indexing schemes have been recently proposed in metric spaces which sort the objects in the database according to pseudo-scores. It is known that (1) some of them provide a very good trade-off between response time and accuracy, and (2) probability-based pseudo-scores can provide an optimal trade-off in range queries if the ...
Takao Murakami +3 more
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On Generalized Contractions in Probabilistic Metric Spaces
AIP Conference Proceedings, 2011In this paper, we introduce a generalized concept of contraction in probabilistic metric spaces. Coincidence and fixed point theorems for mappings with this contraction property are proved and particular cases are analyzed.
Ioan Goleţ +5 more
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Pretopologies, preuniformities and probabilistic metric spaces
Acta Mathematica Hungarica, 2006A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on X form a com- plete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given.
Chicourrat, Monique, Charles, Horvath
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Basic theory and applications of probabilistic metric spaces (II)
Applied Mathematics and Mechanics, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the isometric isomorphism of probabilistic metric spaces
Applied Mathematics and Mechanics, 2002The article is devoted to isomorphisms of probabilistic metric spaces. Two theorems are proved: Theorem 1. If a probabilistic metric space \((E,F)\) is isometrically isomorphic to a generating space of a quasi-metric family, then there is a probabilistic metric space \((E',F')\) such tha t\((E,F)\) is isometrically isomorphic to \((E',F')\). Theorem 2.
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