AN ALGORITHM FOR APPROXIMATING SOLUTIONS OF SPLIT HAMMERSTEIN INTEGRAL EQUATIONS

Abstract

 In this paper, we introduce split Hammerstein integral equations of the form: u ∈ H_1 such

that u + K_1F_1u = 0 and A(u) + K_2F_2(Au) = 0, where K_1, F_1 are maximal monotone maps defined on

a real Hilbert space H_1, with D(K_1) = D(F_1) = H_1; K_2, F_2 are maximal monotone maps defined on a

real Hilbert space H_2, with D(K_2) = D(F_2) = H_2 and A, a bounded linear map from H_1 to H_2. The sequence of the algorithm is proved to converge strongly to a solution of the split Hammerstein integral equation. As far as we know, this is the first algorithm whose sequence approximates a solution of a split Hammerstein integral equation in this direction. Finally, the theorem proved, improves and complements some important related recent results in the literature.