Solution of nonlinear integral equations of Hammerstein type

Let EE be a 22-uniformly real Banach space and F,K:E→EF,K:E→E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u+KFu=0u+KFu=0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is proved. The operators FF and KK are not required to satisfy the so-called range condition. No invertibility assumption is imposed on the operator KK and FF is not restricted to be an angle-bounded (necessarily linear) operator.