PUTNAM EXAM CHALLENGE
Let , where are real numbers and where n is a positive integer. Given that for all real x prove that .
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Let f be a twice-differentiable real-valued function satisfying where for all real x. Prove that is bounded.
Prove that if is a convergent series of positive real
numbers, then so is
Let be a function such that
for all real numbers x. y, and ?. Prove that there exists a function such that
for all real numbers x and y.