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.