Completeness results in probabilistic metric spaces

Alimohammady, Mohsen; Esmaeli, Abdolreza; Saadati, Reza

doi:10.1016/j.chaos.2007.01.072

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Cited by 4 publications

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“…Completeness as well as relations between completeness and fixed point results in probabilistic metric spaces are explored in the papers [4], [8], [62], [68]. We do not enter into the details of this matter.…”

Section: Tataru Distancementioning

confidence: 99%

Fixed points and completeness in metric and in generalized metric spaces

Cobzaş

2015

Preprint

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The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present various circumstances in which fixed point results imply completeness. For metric spaces this is the case of Ekeland variational principle and of its equivalent -Caristi fixed point theorem. Other fixed point results having this property will be also presented in metric spaces, in quasi-metric spaces and in partial metric spaces. A discussion on topology and order and on fixed points in ordered structures and their completeness properties is included as well.

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Section: Tataru Distancementioning

confidence: 99%