On multistep Seidel-Newton methods for quasilinear operator equations (Q1373053)

We consider the following operator equation: \[ Ax=Fx, \tag{1} \] where \(A\) is a bounded linear Fredholm operator (index zero) and \(F\) is a nonlinear operator from a Banach space \(X\) to another Banach space \(Y\). We study equation (1) by using two multistep Seidel-Newton methods, and we show that under some assumptions on \(F\) the rate of convergence of the approximate solutions to the exact one is quadratic.