Sequences and its properties on type-metric space

Abstract

In this paper, we generalized concept of metric space, namely the type-metric space. The difference between type-metric with metric is triangular inequalities. We will investigate some properties of the convergent sequence, the Cauchy sequence, the contractive sequence on the type-metric space. Then, we investigate the relationship between the metric space and the type-metric space with an the example. At the end of this paper, we construct a type-metric function on the cone metric space.