Algorithm for approximating solutions of Hammerstein integral equations with maximal monotone operators (Q1701548)

This paper is devoted to the Hammerstein integral equation of the following type \[ u+KFu=0, \tag{1} \] where \[ Fu(y)=f(y,u(y)), \quad Kv(x)= \int_{\Omega}k(x,y)v(y)dy, \quad x\in\Omega\subset\mathbb{R}^n. \] Here \(k:\Omega\times\Omega\to\mathbb{R}\) and \(f:\Omega\times\mathbb{R}\to\mathbb{R}\) are known measurable real-valued functions. The bounded monotone mappings \(F\) and \(K\) is chosen such that the Hammerstein equation (1) has a solution. An explicit iteration sequence which strongly converges to this solution is then constructed.