Continuous solutions of an iterative-difference equation and Brillou¨et-Belluot�s

• Autores: Yingying Zeng, Weinian Zhang
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 3-4, 2011, págs. 613-624
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4802
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• Resumen

  • It is an open problem proposed by N. Brillou¨et-Belluot to solve the equation f2(x) = f(x+a)..x. Although some related results have been obtained, the problem has remained open. In this paper we prove that it has no continuous real solutions, finally answering Brillou¨et-Belluot�s problem. Furthermore, we give existence of continuous real solutions for the general equation f2(x) = f(x + a) + x on the whole R in some cases which neither include the equation f2(x) = f(x + a) .. x nor are considered in [J. Difference Equ. Appl. 16(11) (2010), 1237�1255].