it is about mathematical analysis

3.Polya's theorem. Yes for each n E N the function f, : I -> R is monotonously increasing and if f (x) = lim -yo (f, (X)) is continuous in / then the convergence is uniform in I4. Suppose that f : R -> R is uniformly continuous in R and for each n E N and x E R let be fn (x ) = f xt .Prove that f, converges uniformly in Ra f n