A Graphical Suprametric Approach to Dynamic Market Structures

Abdurrahman Büyükkaya, Ekber Girgin, Haroon Ahmad, Mudasir Younis and Mahpeyker Öztürk ()
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Abdurrahman Büyükkaya: Department of Mathematics, Karadeniz Technical University, Trabzon 61080, Türkiye
Ekber Girgin: Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, Sakarya 54050, Türkiye
Haroon Ahmad: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Mudasir Younis: Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye
Mahpeyker Öztürk: Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye

Mathematics, 2025, vol. 13, issue 21, 1-25

Abstract: 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.

Keywords: graphically extended suprametric spaces; fixed-point theorems; graphical contractions; dynamic market equilibrium; nonlinear integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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