A pair of functional inequalities characterizing polynomials and Bernoulli numbers

• Autores: Dorota Krassowska, Tomasz Malolepszy, Janusz Matkowski
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 75, Nº. 3, 2008, págs. 276-288
• Idioma: inglés
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• Resumen

  • We show that if a function continuous at least at one point satisfies the pair of functional inequalities and the constants a, b, a i , ß 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.