Residual ν-metric space and Banach contraction principle

Abstract

The purpose of this article is to introduce the concept of residual ν-metric space as a synthesis of a type of generalization of metric space and its extensions namely, b-metric space, extended b-metric space, strong b-metric space, strong controlled b-metric space, double controlled metric type space, suprametric space, b-suprametric space, rectangular metric space, rectangular b-metric space, extended rectangular b-metric space, homothetic rectangular metric space, controlled rectangular b-metric space, ν-generalized metric space and b_ν(s)-metric space. Moreover we give a general form of the notion of contraction in a residual ν-metric space and we prove the analogue of the Banach Contraction Principle in this new framework.