Some fixed point results in function weighted metric spaces (Q2036051)

Summary: After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of \(\mathcal{F}\)-metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of \(\mathcal{F}\)-metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole \(\mathcal{F}\)-metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole \(\mathcal{F}\)-metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.