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].© BrainMass Inc. brainmass.com March 4, 2021, 6:07 pm ad1c9bdddf
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From the condition, we know is differentiable on for each and ...
Uniform convergence is investigated. The differentiable functions for uniformly converges are given.