Iterative solution of nonlinear equations with strongly accretive operators
This article deals with the equation \(Tx=f\) in a real Banach space \(E\) whose dual space is uniformly convex. Under assumptions that the map \(T\) is continuous, strongly accretive, and that \(I-T\) has a bounded range, the convergence is proved of both the Ishikawa and Mann iteration processes to the unique solution of \(Tx=f\). This basic result essentially generalizes earlier results of the author. In addition some explicit error estimates are presented; these estimates are useful for certain choices of the iteration parameters in order to have approximations to the exact solution with prescribed exactness.
scientific article; zbMATH DE number 785127