(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Thepaper represents the concept of a new type of cone metric space known as double composed- cone-metric-like space. It is a generalization of the notion of a double composed-cone-metric space, where in the new space the self-distance is not necessarily zero; meanwhile if the distance metric equals zero, it must be for identical points of distance. Moreover, this context introduces many results related to this novel concept in the literature, with proving some theorems showing that the existence of common fixed points for two maps holds generalized non-linear rational contractions in the proposed new space. Some examples establish the main results and relationship with other cone metric spaces. Finally, this paper demonstrates applications to the nonlinear integral equation and boundary value problem to support the work results.