Strong convergence of inertial shrinking projection method for split best proximity point problem and mixed equilibrium problem

In this paper, we introduce an inertial shrinking projection algorithm to approximate a solution of the best proximity point problem in such a way that the image of its solution under a bounded linear operator is the solution of the mixed equilibrium problem in the framework of real Hilbert spaces. Strong convergence theorem of the proposed algorithm has been established. We also derive some consequences from our main result. Further, we give a numerical experiment to determine the performance and superiority of the proposed algorithm. Finally, a comparison has also been carried out of our algorithm with an existing method.