A new approach to generalize metric functions

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.

Keywords:

φ-metric , φ-metric spaces , generalized distance function , metrizability