Abstract
Very recently, Mehadi et al [M. Asadi, E. Karapmar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on M metric spaces] extended the partial metric spaces to the notion of M metric spaces. In this article, we study some relations between partial metric spaces and M metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to M metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karapmar [E. Karapmar, 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.