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?