A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction
Abstract
In this study, we examine how investors update their price forecasts over time within a "perturbated metric space," which incorporates behavioral influences and market friction. Classical metric structures are inadequate when the measured distance changes with perceived deviations. Therefore, a new structure is proposed in which the measured distance is modified by perceived deviations. In this context, the existence of a fixed point is guaranteed through an extended contraction inequality, and the convergence behavior of the model is analyzed using different examples. Simulations established under different linear and nonlinear update functions demonstrate that the model can reflect both slow and fast market behaviors that reach equilibrium. The proposed approach mathematically demonstrates that investors can reach a common price expectation in the long run, even with heterogeneous psychological responses.
Keywords
References
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Details
Primary Language
English
Subjects
Financial Mathematics, Approximation Theory and Asymptotic Methods, Applied Mathematics (Other)
Journal Section
Research Article
Authors
Publication Date
February 23, 2026
Submission Date
August 8, 2025
Acceptance Date
November 22, 2025
Published in Issue
Year 2026 Volume: 18 Number: 1
APA
Bilazeroğlu, Ş. (2026). A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction. Turkish Journal of Mathematics and Computer Science, 18(1), 32-45. https://doi.org/10.47000/tjmcs.1761322
AMA
1.Bilazeroğlu Ş. A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction. TJMCS. 2026;18(1):32-45. doi:10.47000/tjmcs.1761322
Chicago
Bilazeroğlu, Şeyma. 2026. “A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces With An Extended Contraction”. Turkish Journal of Mathematics and Computer Science 18 (1): 32-45. https://doi.org/10.47000/tjmcs.1761322.
EndNote
Bilazeroğlu Ş (February 1, 2026) A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction. Turkish Journal of Mathematics and Computer Science 18 1 32–45.
IEEE
[1]Ş. Bilazeroğlu, “A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction”, TJMCS, vol. 18, no. 1, pp. 32–45, Feb. 2026, doi: 10.47000/tjmcs.1761322.
ISNAD
Bilazeroğlu, Şeyma. “A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces With An Extended Contraction”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 32-45. https://doi.org/10.47000/tjmcs.1761322.
JAMA
1.Bilazeroğlu Ş. A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction. TJMCS. 2026;18:32–45.
MLA
Bilazeroğlu, Şeyma. “A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces With An Extended Contraction”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 32-45, doi:10.47000/tjmcs.1761322.
Vancouver
1.Şeyma Bilazeroğlu. A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction. TJMCS. 2026 Feb. 1;18(1):32-45. doi:10.47000/tjmcs.1761322