An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces
Keywords:metric, b-metric, $C^*$-algebra-valued metric, $C^*$-algebra-valued b-metric, fixed point.
AbstractWe 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.
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