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


  • Nguyen Van Dung Ton Duc Thang University
  • Vo Thi Le Hang Dong Thap University
  • Diana Dolicanin-Djekic University of Pristina-Kosovska Mitrovica



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


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.


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How to Cite

N. V. Dung, V. T. Le Hang, and D. Dolicanin-Djekic, “An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces”, Appl. Gen. Topol., vol. 18, no. 2, pp. 241–253, Oct. 2017.



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