If f is a function from R to R, and there exists a real number aE(0,1) such that |f'(x)|≤a for all xER , show that the equation x = f(x) has a solution.© BrainMass Inc. brainmass.com March 4, 2021, 7:13 pm ad1c9bdddf
Please see the attached file for the complete solution.
Thanks for using BrainMass.
6. If f is a function from R to R, and there exists a real number such that for all , show that the equation x = f(x) has a solution.
Proof. Consider a sequence defined by
A real analysis proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.