Fixed Points and Completeness in Metric and Generalized Metric Spaces

Cobzaş, Ştefan

doi:10.1007/s10958-020-05027-1

Cited by 19 publications

(15 citation statements)

References 130 publications

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“…For example, in a paper from 1931, Wilson [145] called "quasimetric" the generalized metric obtained from a metric by dropping out the symmetry property, see also Cobzas [45]. For another concept bearing the same name, see Hitzler [74].…”

Section: Origins Of Quasimetric Spaces (B-metric Spaces)mentioning

confidence: 99%

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"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"

Berinde¹,

Pačurar²

2022

CJM

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"A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early developments on fixed point theory in b-metric spaces are though perpetually taking over from the existing publications to the new ones. Starting from this fact, our main aim in this note is threefold: (1) to briefly survey the early developments in the fixed point theory on quasimetric spaces (b-metric spaces); (2) to collect some relevant bibliography related to this topic; (3) to discuss some other aspects of current interest in the fixed point theory on quasimetric spaces (b-metric spaces)."

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Section: Origins Of Quasimetric Spaces (B-metric Spaces)mentioning

confidence: 99%

“…For more details on the metrizability of quasimetric spaces, we refer to [2], [41], [45], [46], [60], [61], [119],...…”

Section: Example 31 (Vulpe Et Allmentioning

confidence: 99%

"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"

Berinde¹,

Pačurar²

2022

CJM

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“…Cobzas [17] also showed the characterization of completeness of uniformly Lipschitz connected metric spaces as given below.…”

Section: Characterization Of Completenessmentioning

confidence: 99%

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

et al. 2021

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The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

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“…The end problem is to determine where and when a human dynamics defined as a succession of positions that starts from an initial position and follows transitions ends. For details on the completeness problem and the end problem, we refer to [33,34] and references therein. In 1959, Connel presented an example ( [35], (Example 3)) (also compare [20]) which shows that BCP does not characterize metric (b−metric) completeness.…”

Section: Introductionmentioning

confidence: 99%

Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

Khan

Ali

2021

Symmetry

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The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of b−metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of b−metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.

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Fixed Points and Completeness in Metric and Generalized Metric Spaces

Cited by 19 publications

References 130 publications

"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"

"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

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