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In this paper, we show that every regular semimetric space having a strong triangle function $$\Phi $$Φ is metrizable if $$\Phi $$Φ is continuous in each of its variables at… Click to show full abstract
In this paper, we show that every regular semimetric space having a strong triangle function $$\Phi $$Φ is metrizable if $$\Phi $$Φ is continuous in each of its variables at (0, 0). We also construct a counterexample to give a negative answer to an open question on such spaces posed in Kirk and Shahzad (J Fixed Point Theory Appl 17(3):541–555, 2015).
Keywords:
semimetric spaces;
strong triangle;
spaces strong;
regular semimetric;
triangle functions
Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2017
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Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!