Completeness and Fixed Points in Probabilistic Quasi-Pseudo-Metric Spaces

Mariusz Grabiec, Yeol Je Cho, Reza Saadati


This paper considers the problem of defining Cauchy sequence and completeness in probabilistic-quasi-pseudo-metric spaces. The definition proposed allow versions of such classical theorems as Baire category theorem, the contraction principle and Cantor’s characterization of completeness to be formulated in the probabilistic-quasi -pseudo-metric setting.


Probabilistic-quasi-pseudo-metric space, Cauchy sequence, completeness, Baire category theorem, contraction principle, fixed points

Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.