Fixed Point Theorems and Applications : Theorems and Applications

Fixed point theory is a fascinating subject with an enormous number of appli-cations in various fields of mathematics. Maybe due to this transversal characterI have always experienced some difficulties to find a book (unless expressly de-voted to fixed points) treating the argument in a unitary fashion. In most casesI noticed that fixed points pop up when they are needed. On the contrary Ibelieve that they should deserve a relevant place in any general textbook andparticularly in a functional analysis textbook. This is mainly the reason thatmade me decide to write down these notes. I tried to collect most of the signifi-cant results of the field and then to present various related applications.A glance of the table of contents will reveal that this textbook treats topics inanalysis at the ”Fixed point theorems and applications” level. The aim has beento provide a development of the subject which is honest rigorous up to date andat the same time not too pedantic. The book provides a transition from ele-mentary differential equations to advanced courses in differential equations andit introduces the reader to some of the abstract thinking that pervades modernanalysis.