VISCOSITY APPROXIMATION FOR SPLIT MONOTONE VARIATIONAL INCLUSIONS AND FIXED POINT PROBLEM

In this work, we investigate an iterative method based on viscosity approximation method to approximate a common solution of split monotone variational inclusion problem and fixed point problem for a nonexpansive mapping in the frame work of real Hilbert spaces. Further, strong convergence theorem is proved by the sequences generated by the proposed iterative method under some mild conditions, which is the unique solution of the variational inequality problem. Furthermore, we provide some numerical experiments to support our main result. The results and method presented in this work may be treated as an improvement, extension and refinement of some corresponding ones in the literature.