Solving a damped spring-mass system via the MA-simulation function

Introduction/purpose: In an interesting article, Perveen & Imdad (2019) introduced the notion of an MA-simulation function, and utilized it to prove the existence of a fixed point for a self mapping through a-admisibilty and the continuity of the self-map in a fuzzy metric space. The purpose of this paper is to establish a unique fixed point theorem for an MA-contractive mapping by relaxing the condition of continuity and a-admissibilty of the map in a fuzzy metric space. As an application of our result, we study the existence and uniqueness of the solution to the damped spring-mass system. The article includes an example which shows the validity of our results. Methods: The fixed point method with an MA-simulation function was used. Results: A unique fixed point for a self map in a fuzzy metric space is obtained. Conclusions: A fixed point of the self map is obtained without the continuity and a-admissibility of the self map via the MA-simulation function. Also, the existence and uniqueness of the solution of a damped spring-mass system in the setting of a fuzzy metric space is obtained.