Explore BrainMass

Explore BrainMass

    Real analysis: Existence Of A Fixed Point

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let f be a continuous function on the closed interval [0,1] with range also contained in [0,1].Prove that f must have a fixed point; that is, show f(x)=x for at least one value of x belong to [0,1].

    © BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf

    Solution Preview

    We consider the function g(x)=f(x)-x
    From the condition, the range of f(x) ...

    Solution Summary

    The solution is comprised of a proof regarding the existence of a fixed point.