Abstract
In this paper, we give an interesting extension of the partial S-metric space which was introduced [N. Mlaiki, Univers. J. Math. Math. Appl., 5 (2014), 109-119] to the M-s -metric space. Also, we prove the existence and uniqueness of a fixed point for a self-mapping on an M-s -metric space under different contraction principles. (C)2017 all rights reserved.