Double Controlled Quasi-Metric Type Spaces and Some Results

Abstract

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.

Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

“…Shoaib et al [35] established results for multivalued functions in a dislocated quasi-metric space, see also [8,37]. Rational type, Kannan type, and Reich type contractions on multivalued functions in double controlled quasi-metric type spaces [34,36] have been introduced, and some fixed point theorems have been obtained. Another generalization of metric space, named function weighted metric space or F-metric space (see, [2][3][4]22]), was defined by Jleli [13].…”