A relaxed splitting method for solving variational inclusion and fixed point problems

In this work, we propose an iterative method for finding a common solution of a variational inclusion problem involving a maximally monotone operator and a fixed point problem for a pseudocontractive mapping in real Hilbert space. Under some standard and easy-to-verify conditions, we establish that the sequence generated by the proposed method converges strongly to a solution of the considered problem. Numerical illustrations and application in image recovery suggest that the proposed method is easy to implement and efficient.