Introduction

In this introductory chapter we give a short account of the contents of the book and discuss simple notions and examples of the fixed point theory to be developed and applied to more involved applications in later chapters. As an introduction to the fixed point theory and its applications let us recall two fixed point theorems on a nonempty closed and bounded subset P of ℝm, one purely topological (Brouwer’s fixed point theorem) and one order-theoretically based. A point $$x\ \epsilon\ P$$ is called a fixed point of a function $$G : P \rightarrow P \ \text {if}\ x = Gx.$$ We assume that ℝm is equipped with Euclidean metric.