Approximation of solutions of generalized equations of Hammerstein type

Abstract

Let E be a 2-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. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation. Our result improves, generalizes and extends the results of Chidume and Ofoedu [C.E. Chidume, E.U. Ofoedu, Solution of nonlinear integral equations of Hammerstein type, Nonlinear Anal. 74 (2011) 4293–4299] and Chidume and Shehu [C.E. Chidume, Y. Shehu, Approximation of solutions of generalized equations of Hammerstein type, Comput. Math. Appl. 63 (2012) 966–974].