Fixed Point Theory

In this chapter we deal with fixed point theory, which is one of the basic mathematical tools in proving the existence of solutions for different types of equations and inclusions. Fixed point theory uses tools from Analysis and Topology and this leads to an informal classification of the results to “metric fixed point theory”(here the metric structure of the ambient space and the metric properties of the maps play a central role), “topological fixed point theory”(here the topological properties of the spaces and/or of the maps are the main tools) and “order fixed point theory”(now the partial order induced by a cone, is the basic ingredient).