On Solutions and Stability of Stochastic Functional Equations Emerging in Psychological Theory of Learning

Abstract

We show how to apply the well-known fixed-point approach in the study of the existence, uniqueness, and stability of solutions to some particular types of functional equations. Moreover, we also obtain the Ulam stability result for them. The functional equations that we consider can be used to explain various experiments in mathematical psychology and arise in a natural way in the stochastic approach to the processes of perception, learning, reasoning, and cognition.

Keywords

• stochastic functional equations
• mathematical psychology
• Ulam stability
• fixed point