An iterative method for solving nonlinear integral equations of Hammerstein type

作者：Chidume C E^*; Djitte N

来源：Applied Mathematics and Computation, 2013, 219(10): 5613-5621.

DOI：10.1016/j.amc.2012.11.051

• Accretive operators
• Hammerstein equations
• Integral equations

Suppose H is a real Hilbert space and F, K : H -> H are continuous bounded monotone maps with D(K) = D(F) = H. Assume that the Hammerstein equation u + KFu = 0 has a solution. An explicit iteration process is proved to converge strongly to a solution of this equation. No invertibility assumption is imposed on K and the operator F is not restricted to be angle-bounded. Our theorem complements the Galerkin method of Brezis and Browder to provide methods for approximating solutions of nonlinear integral equations of Hammerstein type.

• 出版日期2013-1-15