*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

In this paper, a new concept of generalized quasi-partial metric spaces is presented. Some fixed point results due to Karapinar et. al., [E. Karapinar, I. M. Erhan, A. Öztürk, Math. Comput. Modelling, 57 (2013), 2442–2448] are extended in the setting of the generalized quasi-partial metric spaces. c ©2016 All rights reserved.

In this work, we prove some coupled fixed point theory for ψ-contractive in partial metric spaces which extend and generalize some results on fixed point theorems in ordered partial metric spaces. We also provide an example in support of our main result.

In this paper, we introduce some concepts in partial b-metric spaces. We establish fixed point theorems for some new generalized α − ψ type contractive mappings in the setting of partial b-metric spaces. Some examples are presented to illustrate our obtained results. Finally, we show that the results generalize some recent results. c ©2016 All rights reserved.

We prove the existence of the unique common fixed point theorems for self mappings which are weakly compatible satisfying some contractive conditions on partial metric spaces. Furthermore, we also prove the result on the continuity in the set of common fixed points for self mappings on partial metric spaces.

for all x, y Î X, where : R+ ® R+ is a nondecreasing function such that lim n→∞ φ n(t) = 0 for all t > 0. In 1994, Matthews [4] introduced the notion of a partial metric space and obtained a generalization of Banach’s fixed point theorem for partial metric spaces. Recently, Altun et al. [5] (see also Altun and Sadarangani [6]) gave some generalized versions of the fixed point theorem of Matthew...

Partial metrics, or the equivalent weightable quasi-metrics, have been introduced in [Mat94] as part of the study of the denotational semantics of data flow networks (cf. also [Mat95]). The interest in valuations in connection to Domain Theory derives from e.g. [JP89], [Jon89], [Eda94] and [Hec95]. Connections between partial metrics and valuations have been discussed in the literature, e.g. [O...

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of graph preserving mappings in parametric $N_b$-metric spaces. As some consequences of this study, we obtain several important results in parametric $b$-metric spaces, parametric $S$-metric spaces and parametric $A$-metric spaces. Finally, we provide some illustrative examples to ...