On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

Abstract

Numerous computational and learning theory models have been studied using probabilistic functional equations. Especially in two-choice scenarios, the vast bulk of animal behavior research divides such situations into two different events. They split these actions into two possibilities according to the animals’ progress toward a particular decision. However, reward plays a crucial role in such experiments because, based on the selected side and the food placement, such scenarios may be classified into four distinct categories. This article aims to explore the animals’ reactions to such circumstances by presenting a generic stochastic functional equation. By using the well-known fixed point theory results, we examine the existence, uniqueness, and stability of solutions to the suggested functional equation. Moreover, an example is included to emphasize the significance of our findings.

A Solution of a General Functional Equation Involved in Psychological Theory of Learning and Stability Results

“…Turab recently proposed the following FE [19] to extend the aforementioned model (1.6) to a random interval [ 1 , 2 ] in order to continue the study in [6]:…”