Inspired by the modified iteration method devised by He and Zhu [1], the purpose of this
paper is to present a modified Krasnoselskii iteration via boundary method. A strong convergence
theorem of this iteration for finding minimum norm solution of nonlinear equation of the form
ShðxÞðxÞ ¼ 0, where ShðxÞ is a nonlinear mapping of C into itself and h is a function of C into
½0; 1 is then proved in Hilbert spaces. In the same vein, an application to the stationary problem of seepage theory is also presented. The results of this paper are extensions and improvements of some earlier theorems of Saddeek et al. [2].