A Graphical Suprametric Approach to Dynamic Market Structures

Büyükkaya, Abdurrahman; Girgin, Ekber; Ahmad, Haroon; Younis, Mudasir; Öztürk, Mahpeyker

doi:10.3390/math13213496

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A Graphical Suprametric Approach to Dynamic Market Structures

by

Abdurrahman Büyükkaya

¹

,

Ekber Girgin

²

,

Haroon Ahmad

³

,

Mudasir Younis

^4,5

and

Mahpeyker Öztürk

^4,6,*

¹

Department of Mathematics, Karadeniz Technical University, Trabzon 61080, Türkiye

²

Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, Sakarya 54050, Türkiye

³

Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan

⁴

Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye

⁵

Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India

⁶

Picode Software, Education Training Consultancy Research and Development and Trade Ltd., Co., Sakarya 54050, Türkiye

^*

Author to whom correspondence should be addressed.

Mathematics 2025, 13(21), 3496; https://doi.org/10.3390/math13213496

Submission received: 6 August 2025 / Revised: 14 October 2025 / Accepted: 30 October 2025 / Published: 1 November 2025

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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

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MDPI and ACS Style

Büyükkaya, A.; Girgin, E.; Ahmad, H.; Younis, M.; Öztürk, M. A Graphical Suprametric Approach to Dynamic Market Structures. Mathematics 2025, 13, 3496. https://doi.org/10.3390/math13213496

AMA Style

Büyükkaya A, Girgin E, Ahmad H, Younis M, Öztürk M. A Graphical Suprametric Approach to Dynamic Market Structures. Mathematics. 2025; 13(21):3496. https://doi.org/10.3390/math13213496

Chicago/Turabian Style

Büyükkaya, Abdurrahman, Ekber Girgin, Haroon Ahmad, Mudasir Younis, and Mahpeyker Öztürk. 2025. "A Graphical Suprametric Approach to Dynamic Market Structures" Mathematics 13, no. 21: 3496. https://doi.org/10.3390/math13213496

APA Style

Büyükkaya, A., Girgin, E., Ahmad, H., Younis, M., & Öztürk, M. (2025). A Graphical Suprametric Approach to Dynamic Market Structures. Mathematics, 13(21), 3496. https://doi.org/10.3390/math13213496

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