# Real Analysis : Uniform Convergence

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

Let (f_n) be a sequence of diffrentiable functions defined on the closed interval [a,b] and assume (f'_n) converges uniformly on [a,b]. Prove that if there exists a point xo belong to [a,b] where f_n(xo) is convergent, then (f_n) converges uniformly on [a,b].

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:07 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-uniform-convergence-30035

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Proof:

From the condition, we know is differentiable on for each and ...

#### Solution Summary

Uniform convergence is investigated. The differentiable functions for uniformly converges are given.

$2.49