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

Abstract

The psychological learning theory (PLT) in the formation of moral verdict is represented by the choice-practice paradigm. It involves weighing the effects of various options and choosing one to put into practice. This manuscript is devoted to presenting a general functional equation (FE) for observing animal behavior in such situations. The proposed equation can be used to explain a number of well-known learning and psychological theories. The existence and uniqueness of the solution to a given equation are demonstrated using fixed point (FP) techniques. Furthermore, the stability of the solution to the provided FE is explored in the sense of Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU). Ultimately, to emphasize the importance of our results, two examples are presented.