A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces

Abstract

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 Sh(x)(x)=0, where Sh(x) is a nonlinear mapping of C into itself and h is a function of C into [0,1] 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].

Keywords

• Krasnoselskii iteration
• Strong convergence
• Minimum norm solution
• Pseudomonotone mappings
• Lipschitzian mappings
• Seepage theory