Inertial modified S-iteration method for Cayley inclusion problem and fixed point problem

The primary goal of this paper is to study and examine an inertial modified S-iteration method that combines modified S-iteration with inertial extrapolation term to approximate a common solution of the Cayley inclusion problem and the fixed point problem in the framework of real Hilbert space. Under some modest circumstances, we prove weak and strong convergence theorems. A numerical example is also provided to demonstrate the effectiveness of the proposed iterative algorithm. Finally, a comparison has also been carried out of our algorithm with an existing method.