Double Controlled Quasi-Metric Type Spaces and Some Results

Abstract EN

Abdeljawad et al.

(2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended b-metric spaces.

In this paper, we extend their concept and introduce the concept of double controlled quasi-metric type spaces with two incomparable functions and prove some unique fixed point results involving new types of contraction conditions.

Also, we introduce the concept of α−μ−k double controlled contraction and prove some related fixed point results.

We give several examples to show that our results are the proper generalization of the existing works.