Necessary conditions for the power convergence rate of a class of iterative processes for nonlinear ill-posed operator equations in Banach spaces

We study the rate of convergence of a class of iterative methods for solving nonlinear ill-posed equations with operators possessing sectorial derivatives. It is found that the condition of sourcewise representation for an initial residual with a positive exponent (which is sufficient for power convergence estimates with the same exponent) is actually close to a necessary one and cannot be substantially weakened.