On solutions of inclusion problems and fixed point problems (Q395225)

The paper proposes an iterative algorithm for the solution of the following problem: \[ x= S(x) \text{ and } x\in (A+B)^{-1}(0), \] where \(S:C\to C\) is a mapping and \(A,B:C\to H\) are two monotone mappings on a nonempty, closed, convex subset \(C\) of an Hilbert space \(H\). The main theorems of the paper give strong convergence theorems for a hybrid iterative method with errors. The results of the paper may be compared to the theorems given in [\textit{W. Takahashi} and \textit{M. Toyoda}, J. Optim. Theory Appl. 118, No. 2, 417--428 (2003; Zbl 1055.47052)], where weak convergence results are established.