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Miklós Schweitzer 1954- Problem 3

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September 29, 2015
functionreal analysiscollege contests

Problem Statement

3. Is there a real-valued function AfAf, defined on the space of the functions, continuous on [0,1][0,1], such that f(x)≤g(x)f(x)\leq g(x) andf(x)≢g(x)f(x)\not\equiv g(x) inply Af<AgAf< Ag? Is this also true if the functions f(x)f(x) are required to be monotonically increasing (rather than continuous) on [0,1][0,1]? (R.4)
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