The Asymptotically Regularity and Sequences in Partial Cone b-Metric Spaces with Application

Abstract

Abstract. The aim of this paper is to propose a new space called a cone b-metric space by using both
the notions of cone b-metric spaces and partial metric spaces and by defining asymptotically regular maps
and sequences. We also prove some fixed point theorems for such maps and sequences. Our results extend
and generalize some interesting results of [11] and [21] in partial cone b-metric space. An example is also
given to support the validity of our results.