The Approximate Solution Of Nonlinear Fixed Point Operator Equations In Normed Linear Spaces

The approximate solution of nonlinear fixed point operator equations in normed linear spaces

The report presents a class of new algorithms for the approximate determination of the fixed points of 'operators' in normed linear spaces. The method of averaging functional corrections is itself a generalization of the classical method of successive approximations. Theoretical results concerning the convergence characteristics of the new algorithms are presented. The new methods are shown to be superior to the method of averaging functional corrections for certain types of operators. The primary application is to boundary value problems in integral equation form, and the representation of boundary value problems in this form is discussed. Other potential practical applications are considered. Numerical examples are given which demonstrate that the new algorithms are computational methods of significant practical value. (Author).

The Approximate Solution of Nonlinear Fixed Point Operator Equations in Normed Linear Spaces

Iterative Approximation of Fixed Points

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.