Generalized $\mathrm{\Xi }$-metric-like space and new fixed point results with an application

This paper is devoted to generalizing $\mathrm{\Xi }$-metric spaces and $b$- metric-like spaces to present the structure of generalized $\mathrm{\Xi }$ -metric-like spaces. The topological properties of this space and examples to support it are being investigated. Moreover, as demonstrated in the previous literature, the concept of Lipschitz mappings is presented more generally and some results of fixed points are derived in the aforementioned space. Finally, some theoretical results have been implicated in the discussion of the existence and uniqueness of the solution to the Fredholm integral equation.