Fixed-point theory

Fixed Point Theory is a branch of mathematics that studies the conditions under which a function will map at least one point to itself. In simpler terms, it's about finding points where a given process remains unchanged. For example, if you think of a function as a machine that transforms inputs into outputs, a fixed point is an input that the machine leaves unchanged. This concept is important in various fields, including economics, computer science, and physics, as it helps in understanding equilibrium states, solving equations, and analyzing dynamic systems.