Functional equation modeling of adaptive operant-control systems via Matkowski fixed point theory
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
Plos One
|January 6, 2026
Summary
This study generalizes functional equations for operant-control models without initial conditions. Fixed point theory confirms a unique probabilistic solution, advancing mathematical psychology and behavioral analysis.
Area of Science:
- Mathematical Psychology
- Behavioral Science
- Dynamical Systems Theory
Background:
- Operant-control models are crucial for understanding behavior.
- Existing models often require specific initial conditions, limiting their scope.
- A generalized framework is needed for broader applicability.
Purpose of the Study:
- To present a generalized functional equation for operant-control models.
- To remove the constraint of initial conditions in behavioral modeling.
- To establish a more comprehensive analytical framework.
Main Methods:
- Generalization of functional equations used in operant-control.
- Application of the Matkowski fixed point theorem.
- Development of illustrative examples and simulations.
Main Results:
- A generalized functional equation formulation is proposed.
- Existence and uniqueness of a probabilistic solution are proven.
- Simulations validate the theoretical findings.
Conclusions:
- Fixed point theory offers a robust method for analyzing control-based behavioral models.
- The generalized equation expands the analytical capabilities in mathematical psychology.
- This approach enhances the understanding of operant-control behavior.
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