An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces

We construct a $b$-metric from a given $C^*$-algebra-valued $b$-metric and prove some equivalences between them. Then we show that not only fixed point results but also topological properties on $C^*$-algebra-valued $b$-metric spaces may be deduced from certain results in $b$-metric spaces. In particular, every $C^*$-algebra-valued $b$-metric space is metrizable.

Abstract licence: CC BY-NC-ND

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.