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    Real Analysis : Uniform Convergence

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    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].

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    https://brainmass.com/math/real-analysis/real-analysis-uniform-convergence-30035

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    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.

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