The existence of a Fixed Point is: A) Let g e C[a, b] be

Last updated: 7/15/2022

The existence of a Fixed Point is: A) Let g e C[a, b] be such that g(x) = (a, b), In addition, if g' exists on (a, b) and that a constant 0 <k < 1 exists with lg'(x) s k, for all x = (a, b), then the function g has a unique fixed-point p in [a, b]. B) Let ge C[a, b] be such that g(x) e [a, b]. In addition, if g' exists on (a, b) and that a constant 0 <k < 1 exists with lg(x) s k, for all x € (a, b). then the function f has a unique fixed-point p in [a, b]. OC) Let g = Cla, b) be such that g(x) = [a, b]. In addition, if g' exists on (a, b) and that a constant k> 1 exists with lg'(x)] ≤ k, for all x = (a, b). then the function g has a unique fixed-point p in [a, b]. D) Let g e C(a, b) be such that g(x) = [a, b]. In addition, if g' exists on (a, b) and that a constant k> 1 exists with lg'(x)] s k, for all x € (a, b). then the function g has a unique fixed-point p in [a, b]. E) Let g e Cla, b] be such that g(x) e [a, b]. In addition, if g' exists on (a, b) and that a constant 0 <k < 1 exists with lg'(x) k, for all x € (a, b). then the function g has a unique fixed-point p in [a, b].