A new approach to generalize metric functions

Document Type : Research Paper


Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-731235, Birbhum, West Bengal, India


This article consists of a new concept of generalized metric space, called $\phi$-metric space which is developed by making a suitable modification in the `triangle inequality. The notion of $\phi$-metric generalizes the concept of some existing metrizable generalized spaces like S-metric, b-metric, etc.  It is shown that one can easily construct a $\phi$-metric from those generalized metric functions and the notion of convergence of a sequence on those generalized metric spaces are identical with the respective induced $\phi$-metric spaces. Moreover, $\phi$-metric space is metrizable and its properties are pretty similar to the metric functions. So $\phi$-metric functions substantially may play the role of metric functions. Also, the structure of $\phi$-metric space is studied and some well-known fixed point theorems are established.


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Volume 14, Issue 3
March 2023
Pages 279-298
  • Receive Date: 14 June 2022
  • Revise Date: 02 September 2022
  • Accept Date: 18 September 2022