Best proximity points of (EP)-operators with qualitative analysis and simulation

In this paper, we analyze a Thakur three-step iterative process adapted for the context of non-self-mappings. Based on this iteration, we state and prove the existence of best proximity points for the recently introduced class of (EP)-non-self-mappings. Under certain assumptions, we study the convergence of the considered Thakur process to a best proximity point for the same class of operators. Moreover, we design a CQ-type algorithm which strongly converges to a best proximity point of such kind of mappings. In addition, we present the CQ-variant of the proposed algorithm that strongly converges to a best proximity pair. Some examples and numerical simulations sustain the efficiency of our new algorithms.