Relations Between partial Metric Spaces and M-Metric Spaces, Caristi Kirk's Theorem in Metric Type Spaces
arXiv:1512.06611
Abstract
Very recently, Mehadi et al [M. Asadi, E. Karapınar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on metric spaces] extended the partial metric spaces to the notion of metric spaces. In this article, we study some relations between partial metric spaces and metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karapınar [E. Karapınar, Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011: 4, (2011)]. We close our contribution by introducing some examples to validate and verify our extension results.