Basics from Linear and Nonlinear Functional Analysis

Abstract

In this chapter we collect the basic principles from linear functional analysis needed in the remaining part of the book. We give definitions for different kinds of function spaces such as weighted Lp-spaces and weighted spaces of continuous functions as well as scales of subspaces of them, which are important for our investigations. We also present some concepts concerned with the stability and convergence of operator sequences or, in other words, with numerical or approximation methods for operator equations. Moreover, we recall some basic facts from fixed point theory, namely Banach’s and Schauder’s fixed point theorems, and discuss a few aspects on the convergence of Newton’s iteration method.