Statistical Metrics

Menger, Karl

doi:10.1007/978-3-7091-6045-9_35

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2006

2023

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Cited by 119 publications

(133 citation statements)

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“…Kramosil and Michalek [13] gave a notion of fuzzy metric space which could be considered as a reformulation, in the fuzzy context, of the notion of probabilistic metric space due to Menger [14]. Later, George and Veeramani [2,4] introduced and studied a notion of fuzzy metric space which constitutes a modification of the one due to Kramosil and Michalek.…”

Section: Introductionmentioning

confidence: 99%

Completable fuzzy metric spaces

Gregori

Miñana

Sapena

2017

Topology and its Applications

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Section: Introductionmentioning

confidence: 99%

Completable fuzzy metric spaces

Gregori

Miñana

Sapena

2017

Topology and its Applications

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“…In 1942, Menger [12] initiated the study of PM-spaces and then Sehgal and Bharucha-Reid [16] followed Menger's line of research by using the notion of probabilistic q-contraction. They proved a unique fixed point result, which is an extension of the celebrated Banach's contraction principles [2].…”

Section: Introductionmentioning

confidence: 99%

New multipled common fixed point theorems in Menger PMT-spaces

Ji¹,

Zhu²,

Wu³

2017

J. Nonlinear Sci. Appl.

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In this work, we introduce the notion of Menger probabilistic metric type space, on the other hand, we introduce a more general class of auxiliary functions in contractivity condition, following that, we obtain some multipled common fixed point theorems for a pair of mappings T : X × X · · · × X m-times → X and A : X → X. As an application, we give out an example to demonstrate the validity of the obtained results. c 2017 all rights reserved.

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“…The concept of fuzzy sets was introduced by Zadeh [29] in 1965. In 1975, Kramosil and Michalek [15] gave the notion of fuzzy metric spaces which could be considered as a reformulation, in the fuzzy context, of the notion of probabilistic metric space due to Menger [19]. On the other hand, Fixed point theorems give the conditions under which maps (single or multivalued) have solutions.…”

Section: Introductionmentioning

confidence: 99%