A fixed point approach to study a class of probabilistic functional equations arising in the psychological theory of learning

Many biological and learning theory models have been investigated using probabilistic functional equations. This article focuses on a specific kind of predator–prey relation in which a predator has two prey options, each with a probability of $x$ and $1-x$, respectively. Our aim is to investigate the animal's responses in such situations by proposing a general probabilistic functional equation. The noteworthy fixed-point results are used to investigate the existence, uniqueness, and stability of solutions to the proposed functional equation. An example is also given to illustrate the importance of our results in this area of research.