Iterative approximation of solutions of equations of Hammerstein type in certain Banach spaces

摘要

Let E be a q-uniformly smooth real Banach space. For each i=1,2,…m, let Fi,Ki:E→E be bounded and accretive mappings. Assume that the generalized Hammerstein equation u+∑i=1mKiFiu=0 has a solution in E. Our purpose in this paper is to construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation. Our result generalizes and extends the results of Chidume and Ofoedu (2011) [C.E. Chidume, E.U. Ofoedu, Solution of nonlinear integral equations of Hammerstein type, Nonlinear Anal. 74 (2011) 4293–4299] and Chidume and Shehu (2012) [C.E. Chidume, Y. Shehu, Approximation of solutions of generalized equations of Hammerstein type, Comput. Math. Appl. 63 (2012) 966–974]. Numerical example of our result is also included.