Sufficient conditions for convergence of modified projection-iterative method for equations with weak nonlinearity (Q1174066)

This article deals with some modification of the well-known convergence conditions of the projective-iterate methods to the equation \(x=f+Tx+\lambda Fx\) with operators \(T,F:\mathbb{X}\to\mathbb{X}\) in a Banach space \(\mathbb{X}=U+V\) that is a direct sum of some of its subspaces \(U\) and \(V\). The corresponding approximations are defined by means of the formulas \(x_ k=f+Tz_ k+\lambda F_{k-1}\) where \(z_ k=x_{k-1}+w_ k\), \(w_ k\in U\), \(x_ k-z_ k\in V\).