A Study of Banach Fixed Point Theorem and Applications of The Fixed Point Theorem
Keywords:
The Fixed Point Theorem, Banach Fixed Point Theorem, equilibriumAbstract
The Fixed point of a function is a point in the set such that the function maps that point to itself. In other words, if a function f takes an element x from a set S and maps it to another element f(x) in S, then x is a fixed point of f if and only if f(x) = x.
The theorem has many applications in various fields, including mathematics, economics, and engineering. For example, in economics, the theorem is used to prove the existence of an equilibrium in certain models. In mathematics, it is used to prove the existence of solutions to differential equations. In engineering, it is used to solve nonlinear equations that arise in various design and control problems.
Key Words : The Fixed Point Theorem, Banach Fixed Point Theorem
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