MathDB
Miklos Schweitzer 1975_6

Source: Theory of Functions

December 30, 2008
functionreal analysisreal analysis unsolved

Problem Statement

Let f f be a differentiable real function and let M M be a positive real number. Prove that if |f(x\plus{}t)\minus{}2f(x)\plus{}f(x\minus{}t)| \leq Mt^2 \; \textrm{for all}\ \;x\ \; \textrm{and}\ \;t\ , then |f'(x\plus{}t)\minus{}f'(x)| \leq M|t|. J. Szabados
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