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

Nguyen Van Dung, Vo Thi Le Hang, Diana Dolicanin-Djekic

Abstract

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.

Keywords

metric; b-metric; $C^*$-algebra-valued metric; $C^*$-algebra-valued b-metric; fixed point.

Subject classification

47H10; 54H25; 54D99; 54E99.

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Universitat Politècnica de València

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