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6

Part of 1964 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1964_6

Source:

9/20/2008
Let y1(x) y_1(x) be an arbitrary, continuous, positive function on [0,A] [0,A], where A A is an arbitrary positive number. Let yn+1=2∫0xyn(t)dt  (n=1,2,...) . y_{n+1}=2 \int_0^x \sqrt{y_n(t)}dt \;(n=1,2,...)\ . Prove that the functions yn(x) y_n(x) converge to the function y=x2 y=x^2 uniformly on [0,A] [0,A].
functionintegrationreal analysisreal analysis unsolved