Iterative algorithms for solutions of Hammerstein integral inclusions

摘要

Let H be a real Hilbert space and let F: H → 2H, K: H → H be maps such that F(x) is closed bounded and nonempty for each x ∈ H. Assuming K and F are monotone, bounded and continuous (relative to the Hausdorff metric in case of F) having full domain, an iterative process is constructed and the sequence of the process is proved to converge strongly to a solution of the Hammerstein inclusion provided a solution exists. The process does not require invertibility of K. This work generalizes established results from singlevalued setting to multivalued one.