Functional equation modeling of adaptive operant-control systems via Matkowski fixed point theory
Abstract
This paper presents a generalized form of the functional equation used in operant-control models by removing the requirement for initial conditions. The proposed formulation extends earlier studies in mathematical psychology and provides a broader analytical framework for modeling operant-control behavior. Using the Matkowski fixed point theorem, we prove the existence and uniqueness of a probabilistic solution to the generalized equation. Illustrative examples and simulations are included to demonstrate the validity of the theoretical results. This work shows that fixed point theory can effectively support the formulation and analysis of control-based behavioral models.
Fields of Study & Subjects
Control and Dynamics of Mobile Robots
Advanced Control Systems Optimization
Control Systems and Identification
Publication details
- Journal / source
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Volume
- 21
- Issue
- 1
- Pages
- e0339678–e0339678
- Publication date
- 5 January 2026
- Language
- EN