Splitting algorithms for solving variational inclusions and pseudomonotone variational inequalities

In this paper, we present a splitting method for solving a variational inclusion problem and a pseudomonotone variational inequality problem in a real Hilbert space. This method consists of forward-backward type method and modified extragradient method with self-adaptive techniques. We show that the sequence generated by the splitting method strongly converges to a com-mon solution of the variational inclusion and the pseudomonotone variational inequality.