An Iterative Algorithm for Approximating Solutions of Hammerstein Integral Equations

Abstract

Suppose E is a uniformly smooth real Banach space and F, K: E → E are bounded accretive maps with D(K) = F(E) = E. Assume that the Hammerstein equation u + KFu = 0 has a solution u*. An explicit simple iteration process is shown to converge strongly to u*. No invertibility or continuity assumption is imposed on K. Our theorems are significant improvements on important recent results (e.g. [11]).