Theorems Guaranteeing Fixed Points
There are numerous theorems in different parts of mathematics that guarantee that functions, if they satisfy certain conditions, have at least one fixed point. These are amongst the most basic qualitative results available: such fixed-point theorems that apply in generality provide valuable insights.
Read more about this topic: Fixed Point (mathematics)
Famous quotes containing the words fixed and/or points:
“Nothing stands out so conspicuously, or remains so firmly fixed in the memory, as something which you have blundered.”
—Marcus Tullius Cicero (106–43 B.C.)
“There are good points about all such wars. People forget self. The virtues of magnanimity, courage, patriotism, etc., etc., are called into life. People are more generous, more sympathetic, better, than when engaged in the more selfish pursuits of peace.”
—Rutherford Birchard Hayes (1822–1893)