Summary.
We show that if a function \(f : {\mathbb{R}} \rightarrow {\mathbb{R}}\) continuous at least at one point satisfies the pair of functional inequalities
and the constants a, b, α i , β i (i = 0, 1,…, k) fulfil some general algebraic conditions, then f must be a polynomial. An explicit formula for the solution, involving Bernoulli numbers, is given.
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Manuscript received: August 8, 2006 and, in final form, February 5, 2007.
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Krassowska, D., Małolepszy, T. & Matkowski, J. A pair of functional inequalities characterizing polynomials and Bernoulli numbers. Aequ. math. 75, 276–288 (2008). https://doi.org/10.1007/s00010-007-2920-8
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DOI: https://doi.org/10.1007/s00010-007-2920-8