On Quasi b-Metric Space with index k and fixed point results

The objective of this article is to introduce a new concept of Quasi Metric Space with index k (k-QMS) and to achieve a new fixed point results on it. For this purpose, first we define Cauchy sequence and convergent sequence on k-QMS. It seems that unlike metrizable spaces there is no definite relationship between Convergent and Cauchy sequences. We define different types of Quasi b-complete metric spaces on it. We also produce two types of contraction mapping of Banach type and prove fixed point results in k-QMS. In addition, we use a special type of continuous mapping to prove another fixed point results on two different Quasi b-complete spaces. Moreover, we provide different types of example to support the topological aspects and results produces herein.