A Graphical Suprametric Approach to Dynamic Market Structures

Büyükkaya A., Girgin E., Ahmad H., Younis M., Öztürk M.

Mathematics, cilt.13, sa.21, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 21
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/math13213496
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: dynamic market equilibrium, fixed-point theorems, graphical contractions, graphically extended suprametric spaces, nonlinear integral equations
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.