Abstract
Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is to propose a generic probabilistic functional equation that can cover most of the mathematical models addressed in the existing literature. The notable fixed-point tools are utilized to examine the existence, uniqueness, and stability of the suggested equation’s solution. Two examples are also given to emphasize the significance of our findings.
Highlights
Introduction of LearningSymmetry 2021, 13, 1313.In an animal or human being, the learning phase may often be viewed as a series of choices between multiple possible reactions
The predator–prey analogy is among the most appealing paradigms in a two-choice scenario emerging in mathematical biology
A predator has two possible prey choices, and the solution occurs when the predator is attracted to a particular type of prey
Summary
In an animal or human being, the learning phase may often be viewed as a series of choices between multiple possible reactions. Even in basic repetitive experiments under strictly regulated conditions, preference chains are mostly volatile, recommending that the probability governs the choice of feedback. It is helpful to identify structural adjustments in the series of alternatives that reflect changes in trial-to-trial outcomes. From this perspective, most of the learning analysis explains the probability of a trial-totest occurrence that describes a stochastic mechanism
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