In the first part of this thesis, some basic concepts about metric spaces and their
properties are repeated. A special emphasis is on the completeness of the metric
space. Next we study mappings between metric spaces and define the notion of
a contraction mapping. What follows is a description of the Banach contraction
principle and a proof of this theorem. In the last chapter, some converse results on
the Banach contraction principle are shown.
|
