An iterative algorithm for approximating solutions of Hammerstein equations with monotone maps in Banach spaces

摘要

Let E=Lp, 1 < p < ∞. Let F: E → E* and K: E* → E be strongly monotone and bounded maps. Suppose the Hammerstein equation u+KFu=0 has a solution u*. A coupled iterative process is constructed and proved to converge strongly to u*. Furthermore, our technique of proof is of independent interest.