In the setup of metric spaces, many recent studies established a significant variety of control type mappings and illustrated some fixed point results. To represent various contractivity conditions, Khojasteh et al. have established the idea of a simulation function and came up with certain conclusions about the fixed point. For two nonlinear operators utilizing this type of control function, in this study we explore the existence of the best proximity coincidence point in this study by generalizing the concept of simulation functions. Finally, we applied our results for a new type of nonlinear integral equations.