A new approach to generalize metric functions

This article consists of a new concept of generalized metric space, called ϕ-metric space which is developed by making a suitable modification in the ‘triangle inequality. The notion of ϕ-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 ϕ-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 ϕ-metric spaces. Moreover, ϕ-metric space is metrizable and its properties are pretty similar to the metric functions. So ϕ-metric functions substantially may play the role of metric functions. Also, the structure of ϕ-metric space is studied and some well-known fixed point theorems are established.