In numerical evaluation there is no. of theorems as per their point position.

Brouwer`s fixed point theorem:
“Assume that g(x) is continuous on the closed interval [a, b]. Assume that the interval [a, b] is mapped to itself by g(x), i.e., for any x 2 [a, b], g(x) 2 [a, b]. Then there exists a point c 2 [a, b] such that g(c) = c. The point c is a fixed point of g(x).”