On completeness in strong partial b-metric spaces, strong b-metric spaces and the 0-Cauchy completions.
Moshokoa, Seithuti Ncongwane, Fanyana
Moshokoa, Seithuti
Ncongwane, Fanyana
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Abstract
The purpose of this paper is to introduce a new notion of a strong partial b-metric space, discuss the notions of completeness via variants of Cauchy sequences and provide a 0-Cauchy completion result for the spaces. The class of strong partial b-metric spaces properly lie between the class of strong b-metric spaces and partial b-metric spaces. Finally, we show that the 0-Cauchy completion of a strong partial b-metric space is unique up to isometry. Our completion result coincides with the classical result on the completion of a strong b-metric space. As an application the Banach contraction principle is discussed in this context.
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Date
2019-06-26
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Elsevier
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Keywords
Strong partial b-metric spaces, Strong b-metric spaces, Completeness, Completions