In this paper, we introduce the concepts of partial-quasi k-metric spaces and strongly partial- quasi spaces, their relationship to metric are studied. Furthermore, obtain some results on fixed point theorems in spaces.

We introduce a new type of Caristi’s mapping on partial metric spaces and show that a partial metric space is complete if and only if every Caristi mapping has a fixed point. From this result we deduce a characterization of bicomplete weightable quasi-metric spaces. Several illustrative examples are given.

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

In 1994, S.G. Matthews introduced the notion of a partial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill generalized Matthews’ notion of partial metric, in order to establish connections between these structures and the topological aspects of domain theory. Here, we obtain a Banach fixed point theorem for complete partial me...

‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...