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

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.The publication of this article was funded by the Qatar National Library. The authors highly appreciate the efforts of referees and editor of this paper who helped us to improve it in several places.Scopu

Fixed Point Results Using Ft-Contractions in Ordered Metric Spaces Having t-Property

In this paper, we prove the existence of fixed points of F t -contraction mappings in partially ordered metric spaces not necessarily complete. We require that the ordered metric space has the t-property, which is a new concept introduced recently by Rashid et.al. We also give some examples to illustrate the new concepts and obtained results