A Graphical Suprametric Approach to Dynamic Market Structures

This study presents a concise analytical framework that combines suprametric spaces with directed graph structures to model dynamic market environments. The proposed setting captures hierarchical and asymmetric relations between economic components, providing a more flexible structure than conventional metric frameworks. Within this framework, several types of contractive mappings, such as supra-Kannan, supra-Reich, and supra-Ciric contractions, are defined, and corresponding fixed point theorems are established. The theoretical results are applied to a nonlinear integral equation describing the evolution of prices in production and consumption processes. Under appropriate assumptions, the existence and uniqueness of solutions are guaranteed, and a numerical example demonstrates the convergence and practical importance of the proposed model.