In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said structures, and also generalize the notions of $G$-metric and $G_p$-metric spaces to arbitrary finite dimension. We prove Cauchy mapping theorems and other fixed point theorems for such spaces.
One of the conclusions of Browder (1960) is a parametric version of Brouwer's Fixed Point Theorem, stating that for every continuous function $f : ([0,1] \times X) \to X$, where $X$ is a simplex in a Euclidean space, the set of fixed points of $f$, namely, the set $\{(t,x) \in [0,1] \times X \colon f(t,x) = x\}$, has a connected component whose projection on the first coordinate is $[0,1]$. Browder's (1960) proof relies on the theory of the fixed point index. We provide an alternative proof to Browder's result using Brouwer's Fixed Point Theorem.
Relations Between partial Metric Spaces and M-Metric Spaces, Caristi Kirk's Theorem in $M-$Metric Type Spaces
最近，Mehadi et al [M. Asadi，E. Karapınar，and P. Salimi，New extension of partial度量空间with some fixed-point results on $M-$度量空间]将部分度量空间推广到$M-$度量空间的概念。本文研究了部分度量空间与$M-$度量空间之间的一些关系。同时，我们将Caristi Kirki定理从部分度量空间推广到$M-$度量空间，修正了E. Karapınar [E. Karapınar，Generalizations of Caristi Kirk's Theorem on Partial度量空间，不动点理论应用2011：4，（2011）].最后，我们介绍了一些例子来验证和验证我们的扩展结果。
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that Hausdorff compact partial metric spaces are metrizable. In the second part of this article we discuss the significance of bottom sets of partial metric spaces in fixed point theorems for mappings acting in these spaces.
This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.
In this present article, we etablish some existence results of $φ-$fixed point of a mapping in a $C^{\ast}$-algebra valued metric spaces and we deduce some fixed point theorems in $C^{\ast}$-algebra valued partial metric spaces. Non-trivial examples are further provided to support the hypotheses of our results.
