PUTNAM EXAM CHALLENGE
Find all the continuous positive functions f(x), for , such that
where is a given real number.
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Let , where are real numbers and where n is a positive integer. Given that for all real x prove that .
For each continuous function , let
and
Find the maximum value of over all such functions f.
This problem was composed by the Committee on the Putnam Prize Competition. © The Mathematical Association of America. All rights reserved.
Let f be a twice-differentiable real-valued function satisfying where for all real x. Prove that is bounded.