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

Mariusz Grabiec, Yeol Je Cho, Reza Saadati

Abstract


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.

Keywords


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



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