A new approach in the context of ordered incomplete partial b-metric spaces

Abstract

The main purpose of this paper is to find some fixed point results with a new approach, particularly in those cases where the existing literature remains silent. More precisely, we introduce partial completeness, f-orbitally completeness, a new type of contractions and many other notions. We also ensure the existence of fixed points for non-contraction maps in the class of incomplete partial b-metric spaces. We have reported some examples in support of our results. 2020 Tawseef Rashid et al., published by De Gruyter 2020.