# What is the role of fixed point theorems in modern mathematics?

About Fixed Point Theorems, Wikipedia says:

Results of this kind are amongst the most generally useful in mathematics.

This seems an accurate statement: indeed, there are many journals dedicated exclusively to this topic and many monographs have been published.

• Could you elaborate on why this kind of theorem is important to the development of current mathematical research? In particular, what is the relationship between fixed point theory and analysis?
• Also, could you recommend some self-contained but comprehensive monographs?
• The following link could be of your interest karlin.mff.cuni.cz/~prazak/uceni/101/Literatura/… – mfl Mar 13 '15 at 23:20
• I believe they occur in mathematical economics. – Michael Hardy Mar 13 '15 at 23:33
• The number of papers published reflects the popularity of a mathematical topic, not necessarily its usefulness. But fixed point theorems are useful in economics, among other areas. – bubba Mar 14 '15 at 2:19

• And if you have a fixed point problem and need solutions to $f(x) = x$, there are lots of numerical methods to solve these kinds of equations. – pjs36 Mar 13 '15 at 23:53